id sid tid token lemma pos iajs-3911 1 1 402 402 NUM iajs-3911 1 2 Β© Β© ADP iajs-3911 1 3 2025 2025 NUM iajs-3911 1 4 the the DET iajs-3911 1 5 author(s author(s NOUN iajs-3911 1 6 ) ) PUNCT iajs-3911 1 7 . . PUNCT iajs-3911 2 1 published publish VERB iajs-3911 2 2 by by ADP iajs-3911 2 3 college college NOUN iajs-3911 2 4 of of ADP iajs-3911 2 5 education education NOUN iajs-3911 2 6 for for ADP iajs-3911 2 7 pure pure ADJ iajs-3911 2 8 science science NOUN iajs-3911 2 9 ( ( PUNCT iajs-3911 2 10 ibn ibn PROPN iajs-3911 2 11 al al PROPN iajs-3911 2 12 - - PUNCT iajs-3911 2 13 haitham haitham PROPN iajs-3911 2 14 ) ) PUNCT iajs-3911 2 15 , , PUNCT iajs-3911 2 16 university university NOUN iajs-3911 2 17 of of ADP iajs-3911 2 18 baghdad baghdad PROPN iajs-3911 2 19 . . PUNCT iajs-3911 3 1 this this PRON iajs-3911 3 2 is be AUX iajs-3911 3 3 an an DET iajs-3911 3 4 open open ADJ iajs-3911 3 5 - - PUNCT iajs-3911 3 6 access access NOUN iajs-3911 3 7 article article NOUN iajs-3911 3 8 distributed distribute VERB iajs-3911 3 9 under under ADP iajs-3911 3 10 the the DET iajs-3911 3 11 terms term NOUN iajs-3911 3 12 of of ADP iajs-3911 3 13 the the DET iajs-3911 3 14 creative creative ADJ iajs-3911 3 15 commons common NOUN iajs-3911 3 16 attribution attribution NOUN iajs-3911 3 17 4.0 4.0 NUM iajs-3911 3 18 international international ADJ iajs-3911 3 19 license license NOUN iajs-3911 3 20 estimate estimate VERB iajs-3911 3 21 the the DET iajs-3911 3 22 parameters parameter NOUN iajs-3911 3 23 of of ADP iajs-3911 3 24 exponential exponential ADJ iajs-3911 3 25 - - PUNCT iajs-3911 3 26 rayleigh rayleigh NOUN iajs-3911 3 27 distribution distribution NOUN iajs-3911 3 28 , , PUNCT iajs-3911 3 29 by by ADP iajs-3911 3 30 using use VERB iajs-3911 3 31 bayesian bayesian NOUN iajs-3911 3 32 method method NOUN iajs-3911 3 33 maral maral ADJ iajs-3911 3 34 mohammed1 mohammed1 PROPN iajs-3911 3 35 * * PUNCT iajs-3911 3 36 and and CCONJ iajs-3911 3 37 iden iden PROPN iajs-3911 3 38 hassan2 hassan2 PROPN iajs-3911 3 39 1 1 NUM iajs-3911 3 40 , , PUNCT iajs-3911 3 41 2department 2department NUM iajs-3911 3 42 of of ADP iajs-3911 3 43 mathematics mathematic NOUN iajs-3911 3 44 , , PUNCT iajs-3911 3 45 college college NOUN iajs-3911 3 46 of of ADP iajs-3911 3 47 science science NOUN iajs-3911 3 48 for for ADP iajs-3911 3 49 women woman NOUN iajs-3911 3 50 , , PUNCT iajs-3911 3 51 university university NOUN iajs-3911 3 52 of of ADP iajs-3911 3 53 baghdad baghdad PROPN iajs-3911 3 54 , , PUNCT iajs-3911 3 55 baghdad baghdad PROPN iajs-3911 3 56 , , PUNCT iajs-3911 3 57 iraq iraq PROPN iajs-3911 3 58 . . PUNCT iajs-3911 4 1 * * PUNCT iajs-3911 4 2 corresponding correspond VERB iajs-3911 4 3 author author NOUN iajs-3911 4 4 . . PUNCT iajs-3911 5 1 received receive VERB iajs-3911 5 2 : : PUNCT iajs-3911 5 3 21 21 NUM iajs-3911 5 4 february february NOUN iajs-3911 5 5 2024 2024 NUM iajs-3911 5 6 accepted accept VERB iajs-3911 5 7 : : PUNCT iajs-3911 5 8 8 8 NUM iajs-3911 5 9 may may PROPN iajs-3911 5 10 2024 2024 NUM iajs-3911 5 11 published publish VERB iajs-3911 5 12 : : PUNCT iajs-3911 5 13 20 20 NUM iajs-3911 5 14 april april PROPN iajs-3911 5 15 2025 2025 NUM iajs-3911 5 16 abstract abstract NOUN iajs-3911 5 17 in in ADP iajs-3911 5 18 this this DET iajs-3911 5 19 paper paper NOUN iajs-3911 5 20 , , PUNCT iajs-3911 5 21 point point VERB iajs-3911 5 22 estimation estimation NOUN iajs-3911 5 23 method method NOUN iajs-3911 5 24 for for ADP iajs-3911 5 25 parameters parameter NOUN iajs-3911 5 26 𝛼 𝛼 VERB iajs-3911 5 27 and and CCONJ iajs-3911 5 28 πœ† πœ† PRON iajs-3911 5 29 of of ADP iajs-3911 5 30 the the DET iajs-3911 5 31 parameters parameter NOUN iajs-3911 5 32 of of ADP iajs-3911 5 33 the the DET iajs-3911 5 34 exponential exponential ADJ iajs-3911 5 35 - - PUNCT iajs-3911 5 36 rayleigh rayleigh NOUN iajs-3911 5 37 distribution distribution NOUN iajs-3911 5 38 which which PRON iajs-3911 5 39 have have AUX iajs-3911 5 40 been be AUX iajs-3911 5 41 estimated estimate VERB iajs-3911 5 42 by by ADP iajs-3911 5 43 the the DET iajs-3911 5 44 use use NOUN iajs-3911 5 45 of of ADP iajs-3911 5 46 a a DET iajs-3911 5 47 simulation simulation NOUN iajs-3911 5 48 technique technique NOUN iajs-3911 5 49 by by ADP iajs-3911 5 50 using use VERB iajs-3911 5 51 two two NUM iajs-3911 5 52 bayesian bayesian NOUN iajs-3911 5 53 estimation estimation NOUN iajs-3911 5 54 methods method NOUN iajs-3911 5 55 ; ; PUNCT iajs-3911 5 56 the the DET iajs-3911 5 57 first first ADJ iajs-3911 5 58 bayesian bayesian NOUN iajs-3911 5 59 method method NOUN iajs-3911 5 60 of of ADP iajs-3911 5 61 estimation estimation NOUN iajs-3911 5 62 consists consist VERB iajs-3911 5 63 of of ADP iajs-3911 5 64 lindely lindely ADV iajs-3911 5 65 approximation approximation NOUN iajs-3911 5 66 estimation estimation NOUN iajs-3911 5 67 method method NOUN iajs-3911 5 68 and and CCONJ iajs-3911 5 69 the the DET iajs-3911 5 70 second second ADJ iajs-3911 5 71 bayesian bayesian NOUN iajs-3911 5 72 estimation estimation NOUN iajs-3911 5 73 method method NOUN iajs-3911 5 74 consists consist VERB iajs-3911 5 75 tierney tierney PROPN iajs-3911 5 76 and and CCONJ iajs-3911 5 77 kadane kadane PROPN iajs-3911 5 78 approximation approximation NOUN iajs-3911 5 79 estimation estimation NOUN iajs-3911 5 80 method method NOUN iajs-3911 5 81 to to PART iajs-3911 5 82 estimate estimate VERB iajs-3911 5 83 all all DET iajs-3911 5 84 the the DET iajs-3911 5 85 unknown unknown ADJ iajs-3911 5 86 parameters parameter NOUN iajs-3911 5 87 ( ( PUNCT iajs-3911 5 88 𝛼 𝛼 X iajs-3911 5 89 , , PUNCT iajs-3911 5 90 πœ† πœ† NOUN iajs-3911 5 91 ) ) PUNCT iajs-3911 5 92 of of ADP iajs-3911 5 93 exponential exponential ADJ iajs-3911 5 94 - - PUNCT iajs-3911 5 95 rayleigh rayleigh NOUN iajs-3911 5 96 distribution distribution NOUN iajs-3911 5 97 . . PUNCT iajs-3911 6 1 the the DET iajs-3911 6 2 bayes bayes PROPN iajs-3911 6 3 estimate estimate NOUN iajs-3911 6 4 of of ADP iajs-3911 6 5 the the DET iajs-3911 6 6 unknown unknown ADJ iajs-3911 6 7 parameter parameter NOUN iajs-3911 6 8 is be AUX iajs-3911 6 9 obtained obtain VERB iajs-3911 6 10 by by ADP iajs-3911 6 11 using use VERB iajs-3911 6 12 the the DET iajs-3911 6 13 approximation approximation NOUN iajs-3911 6 14 methods method NOUN iajs-3911 6 15 of of ADP iajs-3911 6 16 lindley lindley NOUN iajs-3911 6 17 ( ( PUNCT iajs-3911 6 18 1980 1980 NUM iajs-3911 6 19 ) ) PUNCT iajs-3911 6 20 and and CCONJ iajs-3911 6 21 tierney tierney PROPN iajs-3911 6 22 and and CCONJ iajs-3911 6 23 kadane kadane PROPN iajs-3911 6 24 ( ( PUNCT iajs-3911 6 25 1986 1986 NUM iajs-3911 6 26 ) ) PUNCT iajs-3911 6 27 . . PUNCT iajs-3911 7 1 comparisons comparison NOUN iajs-3911 7 2 between between ADP iajs-3911 7 3 these these DET iajs-3911 7 4 two two NUM iajs-3911 7 5 methods method NOUN iajs-3911 7 6 were be AUX iajs-3911 7 7 made make VERB iajs-3911 7 8 by by ADP iajs-3911 7 9 employing employ VERB iajs-3911 7 10 mean mean ADJ iajs-3911 7 11 squares square NOUN iajs-3911 7 12 error error NOUN iajs-3911 7 13 criterion criterion NOUN iajs-3911 7 14 . . PUNCT iajs-3911 8 1 applying apply VERB iajs-3911 8 2 a a DET iajs-3911 8 3 simulation simulation NOUN iajs-3911 8 4 technique technique NOUN iajs-3911 8 5 with with ADP iajs-3911 8 6 different different ADJ iajs-3911 8 7 sample sample NOUN iajs-3911 8 8 sizes size NOUN iajs-3911 8 9 , , PUNCT iajs-3911 8 10 these these DET iajs-3911 8 11 methods method NOUN iajs-3911 8 12 are be AUX iajs-3911 8 13 being be AUX iajs-3911 8 14 compared compare VERB iajs-3911 8 15 . . 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PUNCT iajs-3911 10 1 keywords keyword NOUN iajs-3911 10 2 : : PUNCT iajs-3911 10 3 bayesian bayesian NOUN iajs-3911 10 4 method method NOUN iajs-3911 10 5 , , PUNCT iajs-3911 10 6 exponential exponential ADJ iajs-3911 10 7 - - PUNCT iajs-3911 10 8 rayleigh rayleigh NOUN iajs-3911 10 9 distribution distribution NOUN iajs-3911 10 10 , , PUNCT iajs-3911 10 11 tierney tierney PROPN iajs-3911 10 12 and and CCONJ iajs-3911 10 13 kadane kadane PROPN iajs-3911 10 14 approximation approximation NOUN iajs-3911 10 15 bayes bayes PROPN iajs-3911 10 16 estimation estimation NOUN iajs-3911 10 17 method method NOUN iajs-3911 10 18 , , PUNCT iajs-3911 10 19 linedely linedely ADV iajs-3911 10 20 approximation approximation NOUN iajs-3911 10 21 bayes bayes PROPN iajs-3911 10 22 estimation estimation NOUN iajs-3911 10 23 method method NOUN iajs-3911 10 24 , , PUNCT iajs-3911 10 25 simulation simulation NOUN iajs-3911 10 26 technique technique NOUN iajs-3911 10 27 , , PUNCT iajs-3911 10 28 mean mean ADJ iajs-3911 10 29 squares square NOUN iajs-3911 10 30 error error NOUN iajs-3911 10 31 . . PUNCT iajs-3911 11 1 1 1 X iajs-3911 11 2 . . X iajs-3911 11 3 introduction introduction NOUN iajs-3911 11 4 bayesian bayesian NOUN iajs-3911 11 5 methods method NOUN iajs-3911 11 6 have have AUX iajs-3911 11 7 become become VERB iajs-3911 11 8 popular popular ADJ iajs-3911 11 9 statistical statistical ADJ iajs-3911 11 10 procedures procedure NOUN iajs-3911 11 11 in in ADP iajs-3911 11 12 areas area NOUN iajs-3911 11 13 from from ADP iajs-3911 11 14 medicine medicine NOUN iajs-3911 11 15 to to ADP iajs-3911 11 16 engineering engineering NOUN iajs-3911 11 17 ( ( PUNCT iajs-3911 11 18 1 1 NUM iajs-3911 11 19 ) ) PUNCT iajs-3911 11 20 . . 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PUNCT iajs-3911 15 1 several several ADJ iajs-3911 15 2 researchers researcher NOUN iajs-3911 15 3 have have AUX iajs-3911 15 4 worked work VERB iajs-3911 15 5 on on ADP iajs-3911 15 6 the the DET iajs-3911 15 7 bayesian bayesian NOUN iajs-3911 15 8 estimation estimation NOUN iajs-3911 15 9 . . PUNCT iajs-3911 16 1 ferreira ferreira PROPN iajs-3911 16 2 et et PROPN iajs-3911 16 3 al al PROPN iajs-3911 16 4 . . PROPN iajs-3911 17 1 ( ( PUNCT iajs-3911 17 2 5 5 X iajs-3911 17 3 ) ) PUNCT iajs-3911 17 4 proposed propose VERB iajs-3911 17 5 to to PART iajs-3911 17 6 make make VERB iajs-3911 17 7 bayesian bayesian NOUN iajs-3911 17 8 inferences inference NOUN iajs-3911 17 9 for for ADP iajs-3911 17 10 the the DET iajs-3911 17 11 parameters parameter NOUN iajs-3911 17 12 of of ADP iajs-3911 17 13 the the DET iajs-3911 17 14 lomax lomax PROPN iajs-3911 17 15 distribution distribution NOUN iajs-3911 17 16 using use VERB iajs-3911 17 17 non non ADJ iajs-3911 17 18 - - ADJ iajs-3911 17 19 informative informative ADJ iajs-3911 17 20 priors prior NOUN iajs-3911 17 21 . . PUNCT iajs-3911 18 1 mazaal mazaal NOUN iajs-3911 18 2 et et PROPN iajs-3911 18 3 al al PROPN iajs-3911 18 4 . . PROPN iajs-3911 19 1 ( ( PUNCT iajs-3911 19 2 6 6 NUM iajs-3911 19 3 ) ) PUNCT iajs-3911 19 4 compared compare VERB iajs-3911 19 5 weibull weibull PROPN iajs-3911 19 6 stress stress NOUN iajs-3911 19 7 – – PUNCT iajs-3911 19 8 strength strength NOUN iajs-3911 19 9 reliability reliability NOUN iajs-3911 19 10 bayesian bayesian NOUN iajs-3911 19 11 estimators estimator NOUN iajs-3911 19 12 for for ADP iajs-3911 19 13 singly singly ADV iajs-3911 19 14 type type NOUN iajs-3911 19 15 ii ii PROPN iajs-3911 19 16 censored censor VERB iajs-3911 19 17 data datum NOUN iajs-3911 19 18 under under ADP iajs-3911 19 19 different different ADJ iajs-3911 19 20 loss loss NOUN iajs-3911 19 21 functions function NOUN iajs-3911 19 22 awatif awatif NOUN iajs-3911 19 23 . . PUNCT iajs-3911 20 1 al al PROPN iajs-3911 20 2 - - PUNCT iajs-3911 20 3 baldawi baldawi PROPN iajs-3911 20 4 ( ( PUNCT iajs-3911 20 5 7 7 NUM iajs-3911 20 6 ) ) PUNCT iajs-3911 20 7 employed employ VERB iajs-3911 20 8 noninformative noninformative ADJ iajs-3911 20 9 priors prior NOUN iajs-3911 20 10 to to PART iajs-3911 20 11 compare compare VERB iajs-3911 20 12 a a DET iajs-3911 20 13 few few ADJ iajs-3911 20 14 bayesian bayesian NOUN iajs-3911 20 15 estimation estimation NOUN iajs-3911 20 16 with with ADP iajs-3911 20 17 the the DET iajs-3911 20 18 maximum maximum ADJ iajs-3911 20 19 likelihood likelihood NOUN iajs-3911 20 20 doi.org/10.30526/38.2.3911 doi.org/10.30526/38.2.3911 PROPN iajs-3911 20 21 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ PROPN iajs-3911 20 22 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ PROPN iajs-3911 21 1 https://orcid.org/0000-0002-6492-8196 https://orcid.org/0000-0002-6492-8196 PROPN iajs-3911 21 2 mailto:maral.bakth2203m@csw.uobaghdad.edu.iq mailto:maral.bakth2203m@csw.uobaghdad.edu.iq PROPN iajs-3911 21 3 https://orcid.org/0000-0002-6492-8196 https://orcid.org/0000-0002-6492-8196 PROPN iajs-3911 21 4 mailto:idanha_math@csw.uobaghdad.edu.iq mailto:idanha_math@csw.uobaghdad.edu.iq ADJ iajs-3911 21 5 ihjpas ihjpa NOUN iajs-3911 21 6 . . 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PUNCT iajs-3911 24 1 rasheed rasheed NOUN iajs-3911 24 2 ( ( PUNCT iajs-3911 24 3 9 9 NUM iajs-3911 24 4 ) ) PUNCT iajs-3911 24 5 used use VERB iajs-3911 24 6 the the DET iajs-3911 24 7 bayesian bayesian NOUN iajs-3911 24 8 estimation estimation NOUN iajs-3911 24 9 under under ADP iajs-3911 24 10 the the DET iajs-3911 24 11 quadratic quadratic ADJ iajs-3911 24 12 loss loss NOUN iajs-3911 24 13 function function NOUN iajs-3911 24 14 with with ADP iajs-3911 24 15 no no DET iajs-3911 24 16 information information NOUN iajs-3911 24 17 before before ADP iajs-3911 24 18 estimating estimate VERB iajs-3911 24 19 the the DET iajs-3911 24 20 maxwell maxwell PROPN iajs-3911 24 21 distribution distribution NOUN iajs-3911 24 22 parameter parameter NOUN iajs-3911 24 23 . . 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PUNCT iajs-3911 26 1 kalt kalt NOUN iajs-3911 26 2 and and CCONJ iajs-3911 26 3 hussein hussein PROPN iajs-3911 26 4 ( ( PUNCT iajs-3911 26 5 11 11 NUM iajs-3911 26 6 ) ) PUNCT iajs-3911 26 7 used use VERB iajs-3911 26 8 bayesian bayesian NOUN iajs-3911 26 9 estimation estimation NOUN iajs-3911 26 10 for for ADP iajs-3911 26 11 parameters parameter NOUN iajs-3911 26 12 of of ADP iajs-3911 26 13 modified modify VERB iajs-3911 26 14 weibull weibull NOUN iajs-3911 26 15 distribution distribution NOUN iajs-3911 26 16 using use VERB iajs-3911 26 17 tierney tierney PROPN iajs-3911 26 18 and and CCONJ iajs-3911 26 19 kadane kadane PROPN iajs-3911 26 20 approximation approximation NOUN iajs-3911 26 21 method method NOUN iajs-3911 26 22 . . PUNCT iajs-3911 27 1 mohammed mohammed PROPN iajs-3911 27 2 and and CCONJ iajs-3911 27 3 hussein hussein PROPN iajs-3911 27 4 ( ( PUNCT iajs-3911 27 5 12 12 NUM iajs-3911 27 6 ) ) PUNCT iajs-3911 27 7 estimated estimate VERB iajs-3911 27 8 methods method NOUN iajs-3911 27 9 for for ADP iajs-3911 27 10 new new ADJ iajs-3911 27 11 mixture mixture NOUN iajs-3911 27 12 distribution distribution NOUN iajs-3911 27 13 with with ADP iajs-3911 27 14 simulation simulation NOUN iajs-3911 27 15 and and CCONJ iajs-3911 27 16 application application NOUN iajs-3911 27 17 . . PUNCT iajs-3911 28 1 the the DET iajs-3911 28 2 exponential exponential ADJ iajs-3911 28 3 rayleigh rayleigh NOUN iajs-3911 28 4 distribution distribution NOUN iajs-3911 28 5 is be AUX iajs-3911 28 6 obtained obtain VERB iajs-3911 28 7 based base VERB iajs-3911 28 8 on on ADP iajs-3911 28 9 mixed mix VERB iajs-3911 28 10 between between ADP iajs-3911 28 11 cumulative cumulative ADJ iajs-3911 28 12 distribution distribution NOUN iajs-3911 28 13 function function NOUN iajs-3911 28 14 of of ADP iajs-3911 28 15 exponential exponential ADJ iajs-3911 28 16 distribution distribution NOUN iajs-3911 28 17 and and CCONJ iajs-3911 28 18 cumulative cumulative ADJ iajs-3911 28 19 distribution distribution NOUN iajs-3911 28 20 function function NOUN iajs-3911 28 21 of of ADP iajs-3911 28 22 rayleigh rayleigh PROPN iajs-3911 28 23 distributions distribution NOUN iajs-3911 28 24 ( ( PUNCT iajs-3911 28 25 13 13 NUM iajs-3911 28 26 ) ) PUNCT iajs-3911 28 27 . . PUNCT iajs-3911 29 1 the the DET iajs-3911 29 2 probability probability NOUN iajs-3911 29 3 density density NOUN iajs-3911 29 4 function function NOUN iajs-3911 29 5 of of ADP iajs-3911 29 6 the the DET iajs-3911 29 7 exponential exponential ADJ iajs-3911 29 8 - - PUNCT iajs-3911 29 9 rayleigh rayleigh NOUN iajs-3911 29 10 distribution distribution NOUN iajs-3911 29 11 is be AUX iajs-3911 29 12 defined define VERB iajs-3911 29 13 as as ADP iajs-3911 29 14 follows follow VERB iajs-3911 29 15 ( ( PUNCT iajs-3911 29 16 14 14 NUM iajs-3911 29 17 ): ): PUNCT iajs-3911 29 18 𝑓(𝑑 𝑓(𝑑 PROPN iajs-3911 29 19 ; ; PUNCT iajs-3911 29 20 𝛼 𝛼 X iajs-3911 29 21 , , PUNCT iajs-3911 29 22 πœ† πœ† X iajs-3911 29 23 ) ) PUNCT iajs-3911 29 24 = = SYM iajs-3911 29 25 ( ( PUNCT iajs-3911 30 1 𝛼 𝛼 X iajs-3911 30 2 + + CCONJ iajs-3911 31 1 πœ†π‘‘)𝑒 πœ†π‘‘)𝑒 PROPN iajs-3911 31 2 βˆ’ βˆ’ NOUN iajs-3911 31 3 ( ( PUNCT iajs-3911 31 4 𝛼𝑑+ 𝛼𝑑+ NOUN iajs-3911 31 5 πœ† πœ† DET iajs-3911 31 6 2 2 NUM iajs-3911 31 7 𝑑2 𝑑2 NOUN iajs-3911 31 8 ) ) PUNCT iajs-3911 31 9 , , PUNCT iajs-3911 31 10 𝑑 𝑑 PROPN iajs-3911 31 11 β‰₯ β‰₯ NOUN iajs-3911 31 12 0 0 NUM iajs-3911 31 13 ; ; PUNCT iajs-3911 31 14 𝛼 𝛼 X iajs-3911 31 15 , , PUNCT iajs-3911 31 16 πœ† πœ† PROPN iajs-3911 31 17 > > X iajs-3911 31 18 0 0 PUNCT iajs-3911 31 19 ( ( PUNCT iajs-3911 31 20 1 1 X iajs-3911 31 21 ) ) PUNCT iajs-3911 31 22 the the DET iajs-3911 31 23 cumulative cumulative ADJ iajs-3911 31 24 distribution distribution NOUN iajs-3911 31 25 function function NOUN iajs-3911 31 26 ( ( PUNCT iajs-3911 31 27 cdf cdf PROPN iajs-3911 31 28 ): ): PUNCT iajs-3911 31 29 𝐹(𝑑 𝐹(𝑑 NUM iajs-3911 31 30 ) ) PUNCT iajs-3911 31 31 = = SYM iajs-3911 32 1 1 1 NUM iajs-3911 32 2 βˆ’ βˆ’ PROPN iajs-3911 32 3 π‘’βˆ’(𝛼𝑑+ π‘’βˆ’(𝛼𝑑+ NUM iajs-3911 32 4 πœ† πœ† DET iajs-3911 32 5 2 2 NUM iajs-3911 32 6 𝑑2 𝑑2 NOUN iajs-3911 32 7 ) ) PUNCT iajs-3911 32 8 , , PUNCT iajs-3911 32 9 𝑑 𝑑 PROPN iajs-3911 32 10 β‰₯ β‰₯ NOUN iajs-3911 32 11 0 0 NUM iajs-3911 32 12 ; ; PUNCT iajs-3911 32 13 𝛼 𝛼 X iajs-3911 32 14 , , PUNCT iajs-3911 32 15 πœ† πœ† PROPN iajs-3911 32 16 > > X iajs-3911 32 17 0 0 PUNCT iajs-3911 33 1 ( ( PUNCT iajs-3911 33 2 2 2 NUM iajs-3911 33 3 ) ) PUNCT iajs-3911 33 4 and and CCONJ iajs-3911 33 5 the the DET iajs-3911 33 6 survival survival NOUN iajs-3911 33 7 function function NOUN iajs-3911 33 8 is be AUX iajs-3911 33 9 : : PUNCT iajs-3911 33 10 𝑆(𝑑 𝑆(𝑑 ADJ iajs-3911 33 11 ) ) PUNCT iajs-3911 33 12 = = PUNCT iajs-3911 33 13 π‘’βˆ’(𝛼𝑑+ π‘’βˆ’(𝛼𝑑+ PUNCT iajs-3911 33 14 πœ† πœ† DET iajs-3911 33 15 2 2 NUM iajs-3911 33 16 𝑑2 𝑑2 NOUN iajs-3911 33 17 ) ) PUNCT iajs-3911 33 18 , , PUNCT iajs-3911 33 19 𝑑 𝑑 PROPN iajs-3911 33 20 β‰₯ β‰₯ NOUN iajs-3911 33 21 0 0 NUM iajs-3911 33 22 ; ; PUNCT iajs-3911 33 23 𝛼 𝛼 X iajs-3911 33 24 , , PUNCT iajs-3911 33 25 πœ† πœ† PROPN iajs-3911 33 26 > > X iajs-3911 33 27 0 0 PUNCT iajs-3911 33 28 ( ( PUNCT iajs-3911 33 29 3 3 X iajs-3911 33 30 ) ) PUNCT iajs-3911 33 31 the the DET iajs-3911 33 32 hazard hazard NOUN iajs-3911 33 33 function function NOUN iajs-3911 33 34 is be AUX iajs-3911 33 35 : : PUNCT iajs-3911 33 36 β„Ž(𝑑 β„Ž(𝑑 X iajs-3911 33 37 ) ) PUNCT iajs-3911 34 1 = = PRON iajs-3911 34 2 ( ( PUNCT iajs-3911 34 3 𝛼 𝛼 X iajs-3911 34 4 + + X iajs-3911 34 5 πœ†π‘‘ πœ†π‘‘ NOUN iajs-3911 34 6 ) ) PUNCT iajs-3911 34 7 , , PUNCT iajs-3911 34 8 𝑑 𝑑 PROPN iajs-3911 34 9 β‰₯ β‰₯ NOUN iajs-3911 34 10 0 0 NUM iajs-3911 34 11 ; ; PUNCT iajs-3911 34 12 𝛼 𝛼 X iajs-3911 34 13 , , PUNCT iajs-3911 34 14 πœ† πœ† PROPN iajs-3911 34 15 > > X iajs-3911 34 16 0 0 PUNCT iajs-3911 34 17 ( ( PUNCT iajs-3911 34 18 4 4 X iajs-3911 34 19 ) ) PUNCT iajs-3911 34 20 the the DET iajs-3911 34 21 aim aim NOUN iajs-3911 34 22 of of ADP iajs-3911 34 23 this this DET iajs-3911 34 24 paper paper NOUN iajs-3911 34 25 showing show VERB iajs-3911 34 26 how how SCONJ iajs-3911 34 27 to to PART iajs-3911 34 28 derive derive VERB iajs-3911 34 29 and and CCONJ iajs-3911 34 30 estimate estimate VERB iajs-3911 34 31 the the DET iajs-3911 34 32 two two NUM iajs-3911 34 33 parameters parameter NOUN iajs-3911 34 34 ( ( PUNCT iajs-3911 34 35 scale scale NOUN iajs-3911 34 36 ) ) PUNCT iajs-3911 34 37 in in ADP iajs-3911 34 38 exponential exponential ADJ iajs-3911 34 39 - - PUNCT iajs-3911 34 40 rayleigh rayleigh NOUN iajs-3911 34 41 distribution distribution NOUN iajs-3911 34 42 by by ADP iajs-3911 34 43 using use VERB iajs-3911 34 44 two two NUM iajs-3911 34 45 bayesian bayesian NOUN iajs-3911 34 46 estimation estimation NOUN iajs-3911 34 47 methods method NOUN iajs-3911 34 48 , , PUNCT iajs-3911 34 49 linedely linedely ADJ iajs-3911 34 50 approximation approximation NOUN iajs-3911 34 51 method method NOUN iajs-3911 34 52 and and CCONJ iajs-3911 34 53 tierney tierney PROPN iajs-3911 34 54 and and CCONJ iajs-3911 34 55 kadane kadane PROPN iajs-3911 34 56 approximation approximation NOUN iajs-3911 34 57 method method NOUN iajs-3911 34 58 . . PUNCT iajs-3911 35 1 therefore therefore ADV iajs-3911 35 2 , , PUNCT iajs-3911 35 3 finding find VERB iajs-3911 35 4 and and CCONJ iajs-3911 35 5 estimating estimate VERB iajs-3911 35 6 survival survival NOUN iajs-3911 35 7 function function NOUN iajs-3911 35 8 . . PUNCT iajs-3911 36 1 finely finely ADV iajs-3911 36 2 compare compare VERB iajs-3911 36 3 between between ADP iajs-3911 36 4 these these DET iajs-3911 36 5 two two NUM iajs-3911 36 6 methods method NOUN iajs-3911 36 7 to to PART iajs-3911 36 8 find find VERB iajs-3911 36 9 the the DET iajs-3911 36 10 best good ADJ iajs-3911 36 11 method method NOUN iajs-3911 36 12 . . PUNCT iajs-3911 37 1 the the DET iajs-3911 37 2 structure structure NOUN iajs-3911 37 3 of of ADP iajs-3911 37 4 this this DET iajs-3911 37 5 paper paper NOUN iajs-3911 37 6 is be AUX iajs-3911 37 7 as as SCONJ iajs-3911 37 8 follows follow VERB iajs-3911 37 9 : : PUNCT iajs-3911 37 10 in in ADP iajs-3911 37 11 section section NOUN iajs-3911 37 12 two two NUM iajs-3911 37 13 ; ; PUNCT iajs-3911 37 14 study study NOUN iajs-3911 37 15 of of ADP iajs-3911 37 16 bayesian bayesian NOUN iajs-3911 37 17 estimation estimation NOUN iajs-3911 37 18 method method NOUN iajs-3911 37 19 . . PUNCT iajs-3911 38 1 section section NOUN iajs-3911 38 2 three three NUM iajs-3911 38 3 ; ; PUNCT iajs-3911 38 4 derive derive ADJ iajs-3911 38 5 exponential exponential ADJ iajs-3911 38 6 - - PUNCT iajs-3911 38 7 rayleigh rayleigh NOUN iajs-3911 38 8 distribution distribution NOUN iajs-3911 38 9 by by ADP iajs-3911 38 10 using use VERB iajs-3911 38 11 the the DET iajs-3911 38 12 linedely linedely ADJ iajs-3911 38 13 approximation approximation NOUN iajs-3911 38 14 method method NOUN iajs-3911 38 15 . . PUNCT iajs-3911 39 1 section section NOUN iajs-3911 39 2 four four NUM iajs-3911 39 3 ; ; PUNCT iajs-3911 39 4 derive derive ADJ iajs-3911 39 5 exponential exponential ADJ iajs-3911 39 6 - - PUNCT iajs-3911 39 7 rayleigh rayleigh NOUN iajs-3911 39 8 distribution distribution NOUN iajs-3911 39 9 by by ADP iajs-3911 39 10 using use VERB iajs-3911 39 11 the the DET iajs-3911 39 12 tierney tierney NOUN iajs-3911 39 13 and and CCONJ iajs-3911 39 14 kadane kadane PROPN iajs-3911 39 15 approximation approximation NOUN iajs-3911 39 16 method method NOUN iajs-3911 39 17 . . PUNCT iajs-3911 40 1 section section NOUN iajs-3911 40 2 five five NUM iajs-3911 40 3 ; ; PUNCT iajs-3911 40 4 the the DET iajs-3911 40 5 simulation simulation NOUN iajs-3911 40 6 technique technique NOUN iajs-3911 40 7 is be AUX iajs-3911 40 8 discussed discuss VERB iajs-3911 40 9 . . PUNCT iajs-3911 41 1 section section NOUN iajs-3911 41 2 six six NUM iajs-3911 41 3 ; ; PUNCT iajs-3911 41 4 the the DET iajs-3911 41 5 main main ADJ iajs-3911 41 6 results result NOUN iajs-3911 41 7 are be AUX iajs-3911 41 8 discussed discuss VERB iajs-3911 41 9 . . PUNCT iajs-3911 42 1 finally finally ADV iajs-3911 42 2 , , PUNCT iajs-3911 42 3 section section NOUN iajs-3911 42 4 seven seven NUM iajs-3911 42 5 presents present VERB iajs-3911 42 6 the the DET iajs-3911 42 7 conclusions conclusion NOUN iajs-3911 42 8 . . PUNCT iajs-3911 43 1 2 2 X iajs-3911 43 2 . . X iajs-3911 43 3 materials material NOUN iajs-3911 43 4 and and CCONJ iajs-3911 43 5 methods method NOUN iajs-3911 43 6 2.1 2.1 NUM iajs-3911 43 7 . . PUNCT iajs-3911 44 1 bayesian bayesian NOUN iajs-3911 44 2 method method NOUN iajs-3911 44 3 in in ADP iajs-3911 44 4 the the DET iajs-3911 44 5 classical classical ADJ iajs-3911 44 6 estimation estimation NOUN iajs-3911 44 7 methods method NOUN iajs-3911 44 8 assuming assume VERB iajs-3911 44 9 that that SCONJ iajs-3911 44 10 the the DET iajs-3911 44 11 parameters parameter NOUN iajs-3911 44 12 𝛼 𝛼 VERB iajs-3911 44 13 or or CCONJ iajs-3911 44 14 πœ† πœ† PRON iajs-3911 44 15 of of ADP iajs-3911 44 16 any any DET iajs-3911 44 17 distribution distribution NOUN iajs-3911 44 18 was be AUX iajs-3911 44 19 be be AUX iajs-3911 44 20 constant constant ADJ iajs-3911 44 21 and and CCONJ iajs-3911 44 22 fixed fix VERB iajs-3911 44 23 , , PUNCT iajs-3911 44 24 but but CCONJ iajs-3911 44 25 it it PRON iajs-3911 44 26 is be AUX iajs-3911 44 27 known know VERB iajs-3911 44 28 to to ADP iajs-3911 44 29 us we PRON iajs-3911 44 30 , , PUNCT iajs-3911 44 31 then then ADV iajs-3911 44 32 these these DET iajs-3911 44 33 methods method NOUN iajs-3911 44 34 were be AUX iajs-3911 44 35 as as ADP iajs-3911 44 36 classical classical ADJ iajs-3911 44 37 methods method NOUN iajs-3911 44 38 ( ( PUNCT iajs-3911 44 39 15 15 NUM iajs-3911 44 40 ) ) PUNCT iajs-3911 44 41 . . PUNCT iajs-3911 45 1 now now ADV iajs-3911 45 2 describing describe VERB iajs-3911 45 3 another another DET iajs-3911 45 4 approach approach NOUN iajs-3911 45 5 to to PART iajs-3911 45 6 estimate estimate VERB iajs-3911 45 7 the the DET iajs-3911 45 8 parameters parameter NOUN iajs-3911 45 9 which which PRON iajs-3911 45 10 are be AUX iajs-3911 45 11 called call VERB iajs-3911 45 12 bayesian bayesian NOUN iajs-3911 45 13 methods method NOUN iajs-3911 45 14 , , PUNCT iajs-3911 45 15 these these DET iajs-3911 45 16 methods method NOUN iajs-3911 45 17 of of ADP iajs-3911 45 18 estimation estimation NOUN iajs-3911 45 19 are be AUX iajs-3911 45 20 typically typically ADV iajs-3911 45 21 predicated predicate VERB iajs-3911 45 22 on on ADP iajs-3911 45 23 the the DET iajs-3911 45 24 idea idea NOUN iajs-3911 45 25 that that SCONJ iajs-3911 45 26 the the DET iajs-3911 45 27 parameters parameter NOUN iajs-3911 45 28 to to PART iajs-3911 45 29 be be AUX iajs-3911 45 30 estimated estimate VERB iajs-3911 45 31 can can AUX iajs-3911 45 32 be be AUX iajs-3911 45 33 random random ADJ iajs-3911 45 34 variables variable NOUN iajs-3911 45 35 as as SCONJ iajs-3911 45 36 opposed oppose VERB iajs-3911 45 37 to to ADP iajs-3911 45 38 fixed fix VERB iajs-3911 45 39 values value NOUN iajs-3911 45 40 ( ( PUNCT iajs-3911 45 41 16,17 16,17 NUM iajs-3911 45 42 ) ) PUNCT iajs-3911 45 43 . . PUNCT iajs-3911 46 1 these these DET iajs-3911 46 2 bayesian bayesian NOUN iajs-3911 46 3 estimation estimation NOUN iajs-3911 46 4 methods method NOUN iajs-3911 46 5 are be AUX iajs-3911 46 6 based base VERB iajs-3911 46 7 on on ADP iajs-3911 46 8 the the DET iajs-3911 46 9 previous previous ADJ iajs-3911 46 10 information information NOUN iajs-3911 46 11 available available ADJ iajs-3911 46 12 on on ADP iajs-3911 46 13 the the DET iajs-3911 46 14 anonymous anonymous ADJ iajs-3911 46 15 parameter parameter NOUN iajs-3911 46 16 plus plus CCONJ iajs-3911 46 17 the the DET iajs-3911 46 18 information information NOUN iajs-3911 46 19 which which PRON iajs-3911 46 20 come come VERB iajs-3911 46 21 from from ADP iajs-3911 46 22 the the DET iajs-3911 46 23 sample sample NOUN iajs-3911 46 24 observations(18 observations(18 ADJ iajs-3911 46 25 ) ) PUNCT iajs-3911 46 26 . . PUNCT iajs-3911 47 1 a a DET iajs-3911 47 2 loss loss NOUN iajs-3911 47 3 function function NOUN iajs-3911 47 4 is be AUX iajs-3911 47 5 a a DET iajs-3911 47 6 measure measure NOUN iajs-3911 47 7 of of ADP iajs-3911 47 8 the the DET iajs-3911 47 9 amount amount NOUN iajs-3911 47 10 of of ADP iajs-3911 47 11 loss loss NOUN iajs-3911 47 12 resulting result VERB iajs-3911 47 13 from from ADP iajs-3911 47 14 a a DET iajs-3911 47 15 decision decision NOUN iajs-3911 47 16 to to PART iajs-3911 47 17 be be AUX iajs-3911 47 18 made make VERB iajs-3911 47 19 depends depend VERB iajs-3911 47 20 on on ADP iajs-3911 47 21 while while SCONJ iajs-3911 47 22 the the DET iajs-3911 47 23 decision decision NOUN iajs-3911 47 24 to to PART iajs-3911 47 25 be be AUX iajs-3911 47 26 made make VERB iajs-3911 47 27 depends depend VERB iajs-3911 47 28 on on ADP iajs-3911 47 29 πœƒ πœƒ PROPN iajs-3911 47 30 ( ( PUNCT iajs-3911 47 31 19 19 NUM iajs-3911 47 32 ) ) PUNCT iajs-3911 47 33 . . PUNCT iajs-3911 48 1 the the DET iajs-3911 48 2 bayesian bayesian NOUN iajs-3911 48 3 estimation estimation NOUN iajs-3911 48 4 method method NOUN iajs-3911 48 5 has have AUX iajs-3911 48 6 received receive VERB iajs-3911 48 7 a a DET iajs-3911 48 8 lot lot NOUN iajs-3911 48 9 of of ADP iajs-3911 48 10 interest interest NOUN iajs-3911 48 11 recently recently ADV iajs-3911 48 12 for for ADP iajs-3911 48 13 analyzing analyze VERB iajs-3911 48 14 failure failure NOUN iajs-3911 48 15 time time NOUN iajs-3911 48 16 data datum NOUN iajs-3911 48 17 which which PRON iajs-3911 48 18 has have AUX iajs-3911 48 19 mostly mostly ADV iajs-3911 48 20 been be AUX iajs-3911 48 21 proposed propose VERB iajs-3911 48 22 as as ADP iajs-3911 48 23 an an DET iajs-3911 48 24 alternative alternative NOUN iajs-3911 48 25 to to ADP iajs-3911 48 26 that that PRON iajs-3911 48 27 of of ADP iajs-3911 48 28 the the DET iajs-3911 48 29 traditional traditional ADJ iajs-3911 48 30 methods method NOUN iajs-3911 48 31 . . PUNCT iajs-3911 49 1 the the DET iajs-3911 49 2 bayesian bayesian NOUN iajs-3911 49 3 estimate estimate NOUN iajs-3911 49 4 method method NOUN iajs-3911 49 5 employs employ VERB iajs-3911 49 6 both both CCONJ iajs-3911 49 7 the the DET iajs-3911 49 8 https://bsj.uobaghdad.edu.iq/do/search/?q=author%3a%22iden%20h.%20alkanani%22&start=0&context=38131414 https://bsj.uobaghdad.edu.iq/do/search/?q=author%3a%22iden%20h.%20alkanani%22&start=0&context=38131414 PROPN iajs-3911 49 9 https://bsj.uobaghdad.edu.iq/do/search/?q=author%3a%22iden%20h.%20alkanani%22&start=0&context=38131414 https://bsj.uobaghdad.edu.iq/do/search/?q=author%3a%22iden%20h.%20alkanani%22&start=0&context=38131414 PROPN iajs-3911 49 10 ihjpas ihjpas PROPN iajs-3911 49 11 . . PUNCT iajs-3911 50 1 2025,38(2 2025,38(2 PROPN iajs-3911 50 2 ) ) PUNCT iajs-3911 50 3 404 404 NUM iajs-3911 50 4 available available ADJ iajs-3911 50 5 data datum NOUN iajs-3911 50 6 and and CCONJ iajs-3911 50 7 one one NUM iajs-3911 50 8 's 's PART iajs-3911 50 9 prior prior ADJ iajs-3911 50 10 knowledge knowledge NOUN iajs-3911 50 11 of of ADP iajs-3911 50 12 the the DET iajs-3911 50 13 parameters parameter NOUN iajs-3911 50 14 ( ( PUNCT iajs-3911 50 15 20,21 20,21 NUM iajs-3911 50 16 ) ) PUNCT iajs-3911 50 17 . . PUNCT iajs-3911 51 1 the the PRON iajs-3911 51 2 non non ADJ iajs-3911 51 3 - - ADJ iajs-3911 51 4 informative informative ADJ iajs-3911 51 5 prior prior ADV iajs-3911 51 6 in in ADP iajs-3911 51 7 bayesian bayesian NOUN iajs-3911 51 8 estimation estimation NOUN iajs-3911 51 9 can can AUX iajs-3911 51 10 be be AUX iajs-3911 51 11 used use VERB iajs-3911 51 12 when when SCONJ iajs-3911 51 13 one one NUM iajs-3911 51 14 's 's PART iajs-3911 51 15 prior prior ADJ iajs-3911 51 16 knowledge knowledge NOUN iajs-3911 51 17 about about ADP iajs-3911 51 18 the the DET iajs-3911 51 19 parameter parameter NOUN iajs-3911 51 20 is be AUX iajs-3911 51 21 unavailable unavailable ADJ iajs-3911 51 22 ( ( PUNCT iajs-3911 51 23 22 22 NUM iajs-3911 51 24 ) ) PUNCT iajs-3911 51 25 . . PUNCT iajs-3911 52 1 2.2 2.2 NUM iajs-3911 52 2 . . PUNCT iajs-3911 53 1 lindely lindely ADV iajs-3911 53 2 approximation approximation NOUN iajs-3911 53 3 estimation estimation NOUN iajs-3911 53 4 method method NOUN iajs-3911 53 5 this this DET iajs-3911 53 6 method method NOUN iajs-3911 53 7 introduced introduce VERB iajs-3911 53 8 by by ADP iajs-3911 53 9 researcher researcher NOUN iajs-3911 53 10 lindely lindely ADV iajs-3911 53 11 in in ADP iajs-3911 53 12 1980 1980 NUM iajs-3911 53 13 . . PUNCT iajs-3911 54 1 the the DET iajs-3911 54 2 two two NUM iajs-3911 54 3 unknown unknown ADJ iajs-3911 54 4 parameters parameter NOUN iajs-3911 54 5 for for ADP iajs-3911 54 6 the the DET iajs-3911 54 7 exponential exponential ADJ iajs-3911 54 8 - - PUNCT iajs-3911 54 9 rayleigh rayleigh NOUN iajs-3911 54 10 distribution distribution NOUN iajs-3911 54 11 are be AUX iajs-3911 54 12 being be AUX iajs-3911 54 13 estimated estimate VERB iajs-3911 54 14 using use VERB iajs-3911 54 15 the the DET iajs-3911 54 16 lindely lindely ADJ iajs-3911 54 17 approximation approximation NOUN iajs-3911 54 18 method method NOUN iajs-3911 54 19 ( ( PUNCT iajs-3911 54 20 23,24 23,24 NOUN iajs-3911 54 21 ) ) PUNCT iajs-3911 54 22 . . PUNCT iajs-3911 55 1 lindely lindely ADV iajs-3911 55 2 approximated approximate VERB iajs-3911 55 3 the the DET iajs-3911 55 4 ratio ratio NOUN iajs-3911 55 5 of of ADP iajs-3911 55 6 the the DET iajs-3911 55 7 integrals integral NOUN iajs-3911 55 8 which which PRON iajs-3911 55 9 as as ADP iajs-3911 55 10 following follow VERB iajs-3911 55 11 form form NOUN iajs-3911 55 12 ( ( PUNCT iajs-3911 55 13 25 25 NUM iajs-3911 55 14 ): ): PUNCT iajs-3911 55 15 βˆ«π‘€(πœƒ)𝑒𝐿(πœƒ)π‘‘πœƒ βˆ«π‘€(πœƒ)𝑒𝐿(πœƒ)π‘‘πœƒ PROPN iajs-3911 55 16 βˆ«π‘£(πœƒ)𝑒𝐿(πœƒ)π‘‘πœƒ βˆ«π‘£(πœƒ)𝑒𝐿(πœƒ)π‘‘πœƒ X iajs-3911 55 17 ( ( PUNCT iajs-3911 55 18 5 5 NUM iajs-3911 55 19 ) ) PUNCT iajs-3911 55 20 where where SCONJ iajs-3911 55 21 πœƒ πœƒ X iajs-3911 55 22 = = PUNCT iajs-3911 55 23 ( ( PUNCT iajs-3911 55 24 πœƒ1 πœƒ1 PROPN iajs-3911 55 25 , , PUNCT iajs-3911 55 26 πœƒ2 πœƒ2 PROPN iajs-3911 55 27 , , PUNCT iajs-3911 55 28 … … PUNCT iajs-3911 55 29 πœƒπ‘)are πœƒπ‘)are CCONJ iajs-3911 55 30 parameters parameter NOUN iajs-3911 55 31 , , PUNCT iajs-3911 55 32 𝑀(πœƒ 𝑀(πœƒ PROPN iajs-3911 55 33 ) ) PUNCT iajs-3911 55 34 and and CCONJ iajs-3911 55 35 𝑣(πœƒ 𝑣(πœƒ NUM iajs-3911 55 36 ) ) PUNCT iajs-3911 55 37 are be AUX iajs-3911 55 38 any any DET iajs-3911 55 39 arbitrary arbitrary ADJ iajs-3911 55 40 functions function NOUN iajs-3911 55 41 for for ADP iajs-3911 55 42 parameters parameter NOUN iajs-3911 55 43 . . PUNCT iajs-3911 56 1 𝐿(πœƒ 𝐿(πœƒ X iajs-3911 56 2 ) ) PUNCT iajs-3911 56 3 is be AUX iajs-3911 56 4 the the DET iajs-3911 56 5 a a DET iajs-3911 56 6 logarithm logarithm NOUN iajs-3911 56 7 of of ADP iajs-3911 56 8 the the DET iajs-3911 56 9 likeihood likeihood NOUN iajs-3911 56 10 function function NOUN iajs-3911 56 11 . . PUNCT iajs-3911 57 1 suppose suppose VERB iajs-3911 57 2 that that SCONJ iajs-3911 57 3 𝑣(πœƒ 𝑣(πœƒ VERB iajs-3911 57 4 ) ) PUNCT iajs-3911 57 5 is be AUX iajs-3911 57 6 the the DET iajs-3911 57 7 prior prior ADJ iajs-3911 57 8 density density NOUN iajs-3911 57 9 function function NOUN iajs-3911 57 10 of of ADP iajs-3911 57 11 parameters parameter NOUN iajs-3911 57 12 πœƒ πœƒ VERB iajs-3911 57 13 and and CCONJ iajs-3911 57 14 let let VERB iajs-3911 57 15 𝑀(πœƒ 𝑀(πœƒ VERB iajs-3911 57 16 ) ) PUNCT iajs-3911 57 17 = = SYM iajs-3911 57 18 𝑒(πœƒ 𝑒(πœƒ ADJ iajs-3911 57 19 ) ) PUNCT iajs-3911 57 20 βˆ™ βˆ™ PROPN iajs-3911 57 21 𝑣(πœƒ 𝑣(πœƒ NUM iajs-3911 57 22 ) ) PUNCT iajs-3911 57 23 . . PUNCT iajs-3911 58 1 from from ADP iajs-3911 58 2 integrals integral NOUN iajs-3911 58 3 equation equation NOUN iajs-3911 58 4 ( ( PUNCT iajs-3911 58 5 1 1 X iajs-3911 58 6 ) ) PUNCT iajs-3911 58 7 getting get VERB iajs-3911 58 8 the the DET iajs-3911 58 9 posterior posterior ADJ iajs-3911 58 10 expectation expectation NOUN iajs-3911 58 11 which which PRON iajs-3911 58 12 is be AUX iajs-3911 58 13 as as SCONJ iajs-3911 58 14 follows follow VERB iajs-3911 58 15 : : PUNCT iajs-3911 58 16 𝐸[𝑒(πœƒ)|𝑑 𝐸[𝑒(πœƒ)|𝑑 ADV iajs-3911 58 17 ] ] X iajs-3911 58 18 = = SYM iajs-3911 58 19 βˆ«π‘’(πœƒ)𝑣(πœƒ βˆ«π‘’(πœƒ)𝑣(πœƒ PROPN iajs-3911 58 20 ) ) PUNCT iajs-3911 58 21 𝑒𝐿(πœƒ)+𝐺(πœƒ)π‘‘πœƒ 𝑒𝐿(πœƒ)+𝐺(πœƒ)π‘‘πœƒ X iajs-3911 58 22 βˆ«π‘£(πœƒ βˆ«π‘£(πœƒ VERB iajs-3911 58 23 ) ) PUNCT iajs-3911 58 24 𝑒𝐿(πœƒ)+𝐺(πœƒ)π‘‘πœƒ 𝑒𝐿(πœƒ)+𝐺(πœƒ)π‘‘πœƒ X iajs-3911 59 1 = = SYM iajs-3911 59 2 βˆ«π‘’(πœƒ βˆ«π‘’(πœƒ NUM iajs-3911 59 3 ) ) PUNCT iajs-3911 59 4 𝑒𝐿(πœƒ)+𝐺(πœƒ)π‘‘πœƒ 𝑒𝐿(πœƒ)+𝐺(πœƒ)π‘‘πœƒ PROPN iajs-3911 59 5 ∫ ∫ PROPN iajs-3911 59 6 𝑒𝐿(πœƒ)+𝐺(πœƒ)π‘‘πœƒ 𝑒𝐿(πœƒ)+𝐺(πœƒ)π‘‘πœƒ PROPN iajs-3911 59 7 . . PUNCT iajs-3911 60 1 where where SCONJ iajs-3911 60 2 𝐺(πœƒ 𝐺(πœƒ VERB iajs-3911 60 3 ) ) PUNCT iajs-3911 60 4 = = SYM iajs-3911 60 5 log𝑒[𝑣(πœƒ log𝑒[𝑣(πœƒ PROPN iajs-3911 60 6 ) ) PUNCT iajs-3911 60 7 ] ] PUNCT iajs-3911 60 8 the the DET iajs-3911 60 9 likeihood likeihood NOUN iajs-3911 60 10 function function NOUN iajs-3911 60 11 of of ADP iajs-3911 60 12 exponential exponential ADJ iajs-3911 60 13 - - PUNCT iajs-3911 60 14 rayleigh rayleigh NOUN iajs-3911 60 15 distribution distribution NOUN iajs-3911 60 16 is be AUX iajs-3911 60 17 : : PUNCT iajs-3911 60 18 𝐿(πœ† 𝐿(πœ† NUM iajs-3911 60 19 ; ; PUNCT iajs-3911 60 20 𝑑1,𝑑2 𝑑1,𝑑2 PROPN iajs-3911 60 21 , , PUNCT iajs-3911 60 22 … … PUNCT iajs-3911 60 23 , , PUNCT iajs-3911 60 24 𝑑𝑛 𝑑𝑛 NUM iajs-3911 60 25 ) ) PUNCT iajs-3911 60 26 = = SYM iajs-3911 60 27 ∏ ∏ PROPN iajs-3911 60 28 ( ( PUNCT iajs-3911 60 29 𝛼 𝛼 NOUN iajs-3911 60 30 + + NUM iajs-3911 60 31 πœ†π‘‘π‘– πœ†π‘‘π‘– NOUN iajs-3911 60 32 ) ) PUNCT iajs-3911 60 33 𝑒 𝑒 ADP iajs-3911 60 34 βˆ’ βˆ’ PROPN iajs-3911 61 1 ( ( PUNCT iajs-3911 61 2 𝛼𝑑𝑖+ 𝛼𝑑𝑖+ NOUN iajs-3911 61 3 πœ† πœ† NOUN iajs-3911 61 4 2 2 NUM iajs-3911 61 5 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 61 6 2 2 NUM iajs-3911 61 7 ) ) PUNCT iajs-3911 61 8 𝑛 𝑛 PRON iajs-3911 61 9 𝑖=1 𝑖=1 PROPN iajs-3911 61 10 ( ( PUNCT iajs-3911 61 11 6 6 NUM iajs-3911 61 12 ) ) PUNCT iajs-3911 61 13 the the DET iajs-3911 61 14 natural natural ADJ iajs-3911 61 15 algorithm algorithm NOUN iajs-3911 61 16 of of ADP iajs-3911 61 17 likeihood likeihood NOUN iajs-3911 61 18 function function NOUN iajs-3911 61 19 is be AUX iajs-3911 61 20 : : PUNCT iajs-3911 61 21 ln ln ADJ iajs-3911 61 22 𝐿(πœ† 𝐿(πœ† X iajs-3911 61 23 ; ; PUNCT iajs-3911 61 24 𝑑1,𝑑2 𝑑1,𝑑2 PROPN iajs-3911 61 25 , , PUNCT iajs-3911 61 26 … … PUNCT iajs-3911 61 27 , , PUNCT iajs-3911 61 28 𝑑𝑛 𝑑𝑛 NUM iajs-3911 61 29 ) ) PUNCT iajs-3911 61 30 = = PUNCT iajs-3911 61 31 βˆ‘ βˆ‘ PUNCT iajs-3911 61 32 ( ( PUNCT iajs-3911 61 33 𝛼 𝛼 PROPN iajs-3911 61 34 + + NUM iajs-3911 61 35 πœ†π‘‘π‘– πœ†π‘‘π‘– NOUN iajs-3911 61 36 ) ) PUNCT iajs-3911 61 37 βˆ’ βˆ’ PROPN iajs-3911 61 38 𝛼 𝛼 INTJ iajs-3911 61 39 βˆ‘ βˆ‘ PUNCT iajs-3911 61 40 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 61 41 βˆ’ βˆ’ PROPN iajs-3911 61 42 πœ† πœ† DET iajs-3911 61 43 2 2 NUM iajs-3911 61 44 βˆ‘ βˆ‘ PROPN iajs-3911 61 45 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 61 46 2𝑛 2𝑛 PROPN iajs-3911 61 47 𝑖=1 𝑖=1 PUNCT iajs-3911 61 48 𝑛 𝑛 PRON iajs-3911 61 49 𝑖=1 𝑖=1 PUNCT iajs-3911 61 50 𝑛 𝑛 PRON iajs-3911 61 51 𝑖=1 𝑖=1 PROPN iajs-3911 61 52 ( ( PUNCT iajs-3911 61 53 7 7 NUM iajs-3911 61 54 ) ) PUNCT iajs-3911 61 55 to to PART iajs-3911 61 56 apply apply VERB iajs-3911 61 57 this this DET iajs-3911 61 58 method method NOUN iajs-3911 61 59 , , PUNCT iajs-3911 61 60 assuming assume VERB iajs-3911 61 61 the the DET iajs-3911 61 62 prior prior ADJ iajs-3911 61 63 density density NOUN iajs-3911 61 64 function function NOUN iajs-3911 61 65 𝑔1(𝛼 𝑔1(𝛼 NOUN iajs-3911 61 66 ) ) PUNCT iajs-3911 61 67 and and CCONJ iajs-3911 61 68 𝑔2(πœ† 𝑔2(πœ† NUM iajs-3911 61 69 ) ) PUNCT iajs-3911 61 70 for for ADP iajs-3911 61 71 the the DET iajs-3911 61 72 parameters parameter NOUN iajs-3911 61 73 𝛼 𝛼 NOUN iajs-3911 61 74 and and CCONJ iajs-3911 61 75 πœ† πœ† PRON iajs-3911 61 76 respectively respectively ADV iajs-3911 61 77 , , PUNCT iajs-3911 61 78 getting get VERB iajs-3911 61 79 the the DET iajs-3911 61 80 posterior posterior ADJ iajs-3911 61 81 distribution distribution NOUN iajs-3911 61 82 . . PUNCT iajs-3911 62 1 assuming assume VERB iajs-3911 62 2 the the DET iajs-3911 62 3 prior prior ADJ iajs-3911 62 4 density density NOUN iajs-3911 62 5 function function NOUN iajs-3911 62 6 for for ADP iajs-3911 62 7 parameters parameter NOUN iajs-3911 62 8 𝛼 𝛼 VERB iajs-3911 62 9 and and CCONJ iajs-3911 62 10 πœ† πœ† NOUN iajs-3911 62 11 is be AUX iajs-3911 62 12 : : PUNCT iajs-3911 62 13 𝑔1(𝛼 𝑔1(𝛼 NOUN iajs-3911 62 14 ) ) PUNCT iajs-3911 62 15 = = SYM iajs-3911 62 16 { { PUNCT iajs-3911 62 17 πœƒπ‘’βˆ’πœƒπ›Ό πœƒπ‘’βˆ’πœƒπ›Ό X iajs-3911 62 18 𝛼 𝛼 X iajs-3911 62 19 > > X iajs-3911 62 20 0 0 NUM iajs-3911 62 21 0 0 NUM iajs-3911 62 22 0π‘‘β„Žπ‘’π‘Ÿ 0π‘‘β„Žπ‘’π‘Ÿ NUM iajs-3911 62 23 𝑀𝑖𝑠𝑒 𝑀𝑖𝑠𝑒 NOUN iajs-3911 62 24 ( ( PUNCT iajs-3911 62 25 8) 8) NUM iajs-3911 62 26 𝑔2(πœ† 𝑔2(πœ† NOUN iajs-3911 62 27 ) ) PUNCT iajs-3911 62 28 = = NOUN iajs-3911 62 29 { { PUNCT iajs-3911 62 30 πœƒπ‘’βˆ’πœƒπœ† πœƒπ‘’βˆ’πœƒπœ† NOUN iajs-3911 62 31 πœ† πœ† X iajs-3911 62 32 > > X iajs-3911 62 33 0 0 NUM iajs-3911 62 34 0 0 NUM iajs-3911 62 35 0π‘‘β„Žπ‘’π‘Ÿ 0π‘‘β„Žπ‘’π‘Ÿ NUM iajs-3911 62 36 𝑀𝑖𝑠𝑒 𝑀𝑖𝑠𝑒 NOUN iajs-3911 62 37 ( ( PUNCT iajs-3911 62 38 9 9 NUM iajs-3911 62 39 ) ) PUNCT iajs-3911 62 40 the the DET iajs-3911 62 41 joint joint ADJ iajs-3911 62 42 prior prior ADJ iajs-3911 62 43 density density NOUN iajs-3911 62 44 functions function NOUN iajs-3911 62 45 for for ADP iajs-3911 62 46 parameters parameter NOUN iajs-3911 62 47 𝛼 𝛼 VERB iajs-3911 62 48 and and CCONJ iajs-3911 62 49 πœ† πœ† PROPN iajs-3911 62 50 is be AUX iajs-3911 62 51 : : PUNCT iajs-3911 62 52 𝑔(𝛼 𝑔(𝛼 NOUN iajs-3911 62 53 , , PUNCT iajs-3911 62 54 πœ† πœ† NOUN iajs-3911 62 55 ) ) PUNCT iajs-3911 62 56 = = SYM iajs-3911 62 57 𝑔1(𝛼 𝑔1(𝛼 NOUN iajs-3911 62 58 ) ) PUNCT iajs-3911 62 59 βˆ™ βˆ™ PROPN iajs-3911 62 60 𝑔2(πœ† 𝑔2(πœ† NUM iajs-3911 62 61 ) ) PUNCT iajs-3911 62 62 = = NOUN iajs-3911 62 63 πœƒπ‘’βˆ’πœƒπ›Ό πœƒπ‘’βˆ’πœƒπ›Ό X iajs-3911 62 64 βˆ™ βˆ™ PROPN iajs-3911 62 65 πœƒπ‘’βˆ’πœƒπœ† πœƒπ‘’βˆ’πœƒπœ† X iajs-3911 62 66 ( ( PUNCT iajs-3911 62 67 10 10 NUM iajs-3911 62 68 ) ) PUNCT iajs-3911 62 69 the the DET iajs-3911 62 70 natural natural ADJ iajs-3911 62 71 algorithm algorithm NOUN iajs-3911 62 72 of of ADP iajs-3911 62 73 joint joint ADJ iajs-3911 62 74 prior prior ADJ iajs-3911 62 75 density density NOUN iajs-3911 62 76 functions function NOUN iajs-3911 62 77 for for ADP iajs-3911 62 78 parameters parameter NOUN iajs-3911 62 79 𝛼 𝛼 VERB iajs-3911 62 80 and and CCONJ iajs-3911 62 81 πœ† πœ† NOUN iajs-3911 62 82 is be AUX iajs-3911 62 83 : : PUNCT iajs-3911 62 84 ln ln ADJ iajs-3911 62 85 𝑔(𝛼 𝑔(𝛼 PROPN iajs-3911 62 86 , , PUNCT iajs-3911 62 87 πœ† πœ† X iajs-3911 62 88 ) ) PUNCT iajs-3911 62 89 = = SYM iajs-3911 62 90 2 2 NUM iajs-3911 62 91 ln ln NOUN iajs-3911 62 92 πœƒ πœƒ NOUN iajs-3911 62 93 βˆ’ βˆ’ NOUN iajs-3911 62 94 πœƒπ›Ό πœƒπ›Ό VERB iajs-3911 62 95 βˆ’ βˆ’ PROPN iajs-3911 62 96 πœƒπœ† πœƒπœ† ADP iajs-3911 62 97 ( ( PUNCT iajs-3911 62 98 11 11 NUM iajs-3911 62 99 ) ) PUNCT iajs-3911 62 100 by by ADP iajs-3911 62 101 using use VERB iajs-3911 62 102 the the DET iajs-3911 62 103 reverse reverse ADJ iajs-3911 62 104 bayes bayes NOUN iajs-3911 62 105 rule rule NOUN iajs-3911 62 106 in in ADP iajs-3911 62 107 the the DET iajs-3911 62 108 integration integration NOUN iajs-3911 62 109 of of ADP iajs-3911 62 110 the the DET iajs-3911 62 111 prior prior ADJ iajs-3911 62 112 density density NOUN iajs-3911 62 113 function function NOUN iajs-3911 62 114 with with ADP iajs-3911 62 115 the the DET iajs-3911 62 116 likelihood likelihood NOUN iajs-3911 62 117 function function NOUN iajs-3911 62 118 we we PRON iajs-3911 62 119 obtain obtain VERB iajs-3911 62 120 the the DET iajs-3911 62 121 function function NOUN iajs-3911 62 122 of of ADP iajs-3911 62 123 the the DET iajs-3911 62 124 posterior posterior ADJ iajs-3911 62 125 distribution distribution NOUN iajs-3911 62 126 of of ADP iajs-3911 62 127 the the DET iajs-3911 62 128 parameters parameter NOUN iajs-3911 62 129 𝛼 𝛼 NOUN iajs-3911 62 130 and and CCONJ iajs-3911 62 131 πœ† πœ† PROPN iajs-3911 62 132 as as SCONJ iajs-3911 62 133 follows follow VERB iajs-3911 62 134 ( ( PUNCT iajs-3911 62 135 26 26 NUM iajs-3911 62 136 ): ): PUNCT iajs-3911 62 137 𝐻(𝛼 𝐻(𝛼 X iajs-3911 62 138 , , PUNCT iajs-3911 62 139 πœ† πœ† NOUN iajs-3911 62 140 ; ; PUNCT iajs-3911 62 141 𝑑1,𝑑2 𝑑1,𝑑2 PROPN iajs-3911 62 142 , , PUNCT iajs-3911 62 143 … … PUNCT iajs-3911 62 144 , , PUNCT iajs-3911 62 145 𝑑𝑛 𝑑𝑛 NUM iajs-3911 62 146 ) ) PUNCT iajs-3911 62 147 = = SYM iajs-3911 62 148 ∏ ∏ PROPN iajs-3911 62 149 ( ( PUNCT iajs-3911 62 150 𝛼 𝛼 NOUN iajs-3911 62 151 + + NUM iajs-3911 62 152 πœ†π‘‘π‘– πœ†π‘‘π‘– NOUN iajs-3911 62 153 ) ) PUNCT iajs-3911 62 154 𝑒 𝑒 PROPN iajs-3911 62 155 βˆ’π›Ό βˆ’π›Ό PROPN iajs-3911 62 156 βˆ‘ βˆ‘ PROPN iajs-3911 62 157 π‘‘π‘–βˆ’ π‘‘π‘–βˆ’ PUNCT iajs-3911 62 158 πœ† πœ† DET iajs-3911 62 159 2 2 NUM iajs-3911 62 160 βˆ‘ βˆ‘ PROPN iajs-3911 62 161 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 62 162 2𝑛 2𝑛 PROPN iajs-3911 62 163 𝑖=1 𝑖=1 PUNCT iajs-3911 62 164 𝑛 𝑛 DET iajs-3911 62 165 𝑖=1 𝑖=1 PROPN iajs-3911 62 166 πœƒπ‘’βˆ’πœƒπ›Ό πœƒπ‘’βˆ’πœƒπ›Ό X iajs-3911 62 167 βˆ™ βˆ™ PROPN iajs-3911 62 168 πœƒπ‘’βˆ’πœƒπœ† πœƒπ‘’βˆ’πœƒπœ† NOUN iajs-3911 62 169 𝑛 𝑛 PRON iajs-3911 62 170 𝑖=1 𝑖=1 PROPN iajs-3911 62 171 ( ( PUNCT iajs-3911 62 172 12 12 NUM iajs-3911 62 173 ) ) PUNCT iajs-3911 62 174 by by ADP iajs-3911 62 175 employing employ VERB iajs-3911 62 176 the the DET iajs-3911 62 177 quadratic quadratic ADJ iajs-3911 62 178 loss loss NOUN iajs-3911 62 179 function function NOUN iajs-3911 62 180 , , PUNCT iajs-3911 62 181 then then ADV iajs-3911 62 182 the the DET iajs-3911 62 183 bayes bayes PROPN iajs-3911 62 184 estimator estimator NOUN iajs-3911 62 185 as as ADP iajs-3911 62 186 οΏ½ οΏ½ PROPN iajs-3911 62 187 Μ‚ Μ‚ X iajs-3911 62 188 οΏ½ οΏ½ NOUN iajs-3911 62 189 π΅π‘Žπ‘¦π‘’π‘ (𝛼 π΅π‘Žπ‘¦π‘’π‘ (𝛼 NOUN iajs-3911 62 190 , , PUNCT iajs-3911 62 191 πœ† πœ† NOUN iajs-3911 62 192 ) ) PUNCT iajs-3911 62 193 for for ADP iajs-3911 62 194 any any DET iajs-3911 62 195 function function NOUN iajs-3911 62 196 with with ADP iajs-3911 62 197 respect respect NOUN iajs-3911 62 198 to to ADP iajs-3911 62 199 the the DET iajs-3911 62 200 parameters parameter NOUN iajs-3911 62 201 πœ™(𝛼 πœ™(𝛼 NOUN iajs-3911 62 202 , , PUNCT iajs-3911 62 203 πœ† πœ† NOUN iajs-3911 62 204 ) ) PUNCT iajs-3911 62 205 is be AUX iajs-3911 62 206 the the DET iajs-3911 62 207 posterior posterior ADJ iajs-3911 62 208 mean mean NOUN iajs-3911 62 209 for for ADP iajs-3911 62 210 this this DET iajs-3911 62 211 function function NOUN iajs-3911 62 212 . . PUNCT iajs-3911 63 1 the the DET iajs-3911 63 2 squared square VERB iajs-3911 63 3 error error NOUN iajs-3911 63 4 loss loss NOUN iajs-3911 63 5 function function NOUN iajs-3911 63 6 is be AUX iajs-3911 63 7 given give VERB iajs-3911 63 8 by by ADP iajs-3911 63 9 following follow VERB iajs-3911 63 10 : : PUNCT iajs-3911 63 11 πΏπ‘œπ‘ π‘ ( πΏπ‘œπ‘ π‘ ( PUNCT iajs-3911 63 12 οΏ½ οΏ½ PROPN iajs-3911 63 13 Μ‚ Μ‚ SYM iajs-3911 63 14 οΏ½ οΏ½ NOUN iajs-3911 63 15 βˆ’ βˆ’ NOUN iajs-3911 63 16 𝛼 𝛼 NOUN iajs-3911 63 17 ) ) PUNCT iajs-3911 63 18 = = SYM iajs-3911 63 19 ( ( PUNCT iajs-3911 63 20 οΏ½ οΏ½ PROPN iajs-3911 63 21 Μ‚ Μ‚ SYM iajs-3911 63 22 οΏ½ οΏ½ PROPN iajs-3911 63 23 βˆ’ βˆ’ PROPN iajs-3911 63 24 𝛼)2 𝛼)2 PROPN iajs-3911 63 25 ( ( PUNCT iajs-3911 63 26 13 13 NUM iajs-3911 63 27 ) ) PUNCT iajs-3911 63 28 πΏπ‘œπ‘ π‘ ( πΏπ‘œπ‘ π‘ ( ADP iajs-3911 63 29 οΏ½ οΏ½ PROPN iajs-3911 63 30 Μ‚ Μ‚ NUM iajs-3911 63 31 οΏ½ οΏ½ NOUN iajs-3911 63 32 βˆ’ βˆ’ NUM iajs-3911 63 33 πœ† πœ† NOUN iajs-3911 63 34 ) ) PUNCT iajs-3911 63 35 = = SYM iajs-3911 63 36 ( ( PUNCT iajs-3911 63 37 οΏ½ οΏ½ PROPN iajs-3911 63 38 Μ‚ Μ‚ SYM iajs-3911 63 39 οΏ½ οΏ½ NOUN iajs-3911 63 40 βˆ’ βˆ’ NUM iajs-3911 63 41 πœ† πœ† NOUN iajs-3911 63 42 ) ) PUNCT iajs-3911 63 43 2 2 NUM iajs-3911 63 44 ( ( PUNCT iajs-3911 63 45 14 14 NUM iajs-3911 63 46 ) ) PUNCT iajs-3911 63 47 the the DET iajs-3911 63 48 bayes bayes PROPN iajs-3911 63 49 estimators estimator NOUN iajs-3911 63 50 for for ADP iajs-3911 63 51 𝛼 𝛼 PRON iajs-3911 63 52 and and CCONJ iajs-3911 63 53 πœ† πœ† NOUN iajs-3911 63 54 for for ADP iajs-3911 63 55 exponential exponential ADJ iajs-3911 63 56 - - PUNCT iajs-3911 63 57 rayleigh rayleigh NOUN iajs-3911 63 58 distribution distribution NOUN iajs-3911 63 59 under under ADP iajs-3911 63 60 squared square VERB iajs-3911 63 61 error error NOUN iajs-3911 63 62 loss loss NOUN iajs-3911 63 63 function function NOUN iajs-3911 63 64 is be AUX iajs-3911 63 65 the the DET iajs-3911 63 66 posterior posterior ADJ iajs-3911 63 67 which which PRON iajs-3911 63 68 given give VERB iajs-3911 63 69 as as ADP iajs-3911 63 70 follows follow VERB iajs-3911 63 71 : : PUNCT iajs-3911 63 72 οΏ½ οΏ½ PROPN iajs-3911 63 73 Μ‚ Μ‚ NOUN iajs-3911 63 74 οΏ½ οΏ½ NOUN iajs-3911 63 75 π΅π‘Žπ‘¦π‘’π‘  π΅π‘Žπ‘¦π‘’π‘  NOUN iajs-3911 63 76 = = PUNCT iajs-3911 63 77 𝐸[𝛼 𝐸[𝛼 NOUN iajs-3911 63 78 , , PUNCT iajs-3911 63 79 πœ† πœ† X iajs-3911 63 80 ] ] X iajs-3911 63 81 = = PUNCT iajs-3911 63 82 βˆ«βˆ«πœ™(𝛼,πœ†)𝐻(𝛼,πœ†;𝑑1,𝑑2, βˆ«βˆ«πœ™(𝛼,πœ†)𝐻(𝛼,πœ†;𝑑1,𝑑2, X iajs-3911 63 83 … … PUNCT iajs-3911 63 84 ,𝑑𝑛)𝑑𝛼 ,𝑑𝑛)𝑑𝛼 PUNCT iajs-3911 63 85 π‘‘πœ† π‘‘πœ† ADP iajs-3911 63 86 ∫∫𝐻(𝛼,πœ†;𝑑1,𝑑2, ∫∫𝐻(𝛼,πœ†;𝑑1,𝑑2, ADP iajs-3911 63 87 … … PUNCT iajs-3911 63 88 ,𝑑𝑛)𝑑𝛼 ,𝑑𝑛)𝑑𝛼 PUNCT iajs-3911 63 89 π‘‘πœ† π‘‘πœ† ADP iajs-3911 63 90 ( ( PUNCT iajs-3911 63 91 15 15 NUM iajs-3911 63 92 ) ) PUNCT iajs-3911 63 93 ihjpas ihjpa NOUN iajs-3911 63 94 . . PUNCT iajs-3911 64 1 2025,38(2 2025,38(2 PROPN iajs-3911 64 2 ) ) PUNCT iajs-3911 64 3 405 405 NUM iajs-3911 64 4 οΏ½ οΏ½ NOUN iajs-3911 64 5 Μ‚ Μ‚ NOUN iajs-3911 64 6 οΏ½ οΏ½ NOUN iajs-3911 64 7 π΅π‘Žπ‘¦π‘’π‘  π΅π‘Žπ‘¦π‘’π‘  NOUN iajs-3911 64 8 = = PUNCT iajs-3911 64 9 𝐸[𝛼 𝐸[𝛼 NOUN iajs-3911 64 10 , , PUNCT iajs-3911 64 11 πœ† πœ† X iajs-3911 64 12 ] ] X iajs-3911 64 13 = = SYM iajs-3911 64 14 βˆ«βˆ«πœ™(𝛼,πœ†)∏ βˆ«βˆ«πœ™(𝛼,πœ†)∏ PROPN iajs-3911 64 15 ( ( PUNCT iajs-3911 64 16 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 64 17 ) ) PUNCT iajs-3911 64 18 𝑒 𝑒 PROPN iajs-3911 64 19 βˆ’π›Ό βˆ’π›Ό PROPN iajs-3911 64 20 βˆ‘ βˆ‘ PROPN iajs-3911 64 21 π‘‘π‘–βˆ’ π‘‘π‘–βˆ’ PUNCT iajs-3911 64 22 πœ† πœ† DET iajs-3911 64 23 2 2 NUM iajs-3911 64 24 βˆ‘ βˆ‘ PROPN iajs-3911 64 25 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 64 26 2𝑛 2𝑛 PROPN iajs-3911 64 27 𝑖=1 𝑖=1 PUNCT iajs-3911 64 28 𝑛 𝑛 PRON iajs-3911 64 29 𝑖=1 𝑖=1 PROPN iajs-3911 64 30 πœƒπ‘’βˆ’πœƒπ›Όβˆ™πœƒπ‘’βˆ’πœƒπœ† πœƒπ‘’βˆ’πœƒπ›Όβˆ™πœƒπ‘’βˆ’πœƒπœ† VERB iajs-3911 64 31 𝑛 𝑛 PRON iajs-3911 64 32 𝑖=1 𝑖=1 PUNCT iajs-3911 64 33 𝑑𝛼 𝑑𝛼 NOUN iajs-3911 64 34 π‘‘πœ† π‘‘πœ† VERB iajs-3911 64 35 ∫∫∏ ∫∫∏ NUM iajs-3911 64 36 ( ( PUNCT iajs-3911 64 37 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 64 38 ) ) PUNCT iajs-3911 64 39 𝑒 𝑒 PROPN iajs-3911 64 40 βˆ’π›Όβˆ‘ βˆ’π›Όβˆ‘ PROPN iajs-3911 64 41 π‘‘π‘–βˆ’ π‘‘π‘–βˆ’ PUNCT iajs-3911 64 42 πœ† πœ† DET iajs-3911 64 43 2 2 NUM iajs-3911 64 44 βˆ‘ βˆ‘ PROPN iajs-3911 64 45 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 64 46 2𝑛 2𝑛 PROPN iajs-3911 64 47 𝑖=1 𝑖=1 PUNCT iajs-3911 64 48 𝑛 𝑛 PRON iajs-3911 64 49 𝑖=1 𝑖=1 PROPN iajs-3911 64 50 πœƒπ‘’βˆ’πœƒπ›Όβˆ™πœƒπ‘’βˆ’πœƒπœ† πœƒπ‘’βˆ’πœƒπ›Όβˆ™πœƒπ‘’βˆ’πœƒπœ† VERB iajs-3911 64 51 𝑛 𝑛 PRON iajs-3911 64 52 𝑖=1 𝑖=1 PROPN iajs-3911 64 53 𝑑𝛼 𝑑𝛼 NOUN iajs-3911 64 54 π‘‘πœ† π‘‘πœ† VERB iajs-3911 64 55 ( ( PUNCT iajs-3911 64 56 16 16 NUM iajs-3911 64 57 ) ) PUNCT iajs-3911 64 58 where where SCONJ iajs-3911 64 59 the the DET iajs-3911 64 60 number number NOUN iajs-3911 64 61 of of ADP iajs-3911 64 62 integrals integral NOUN iajs-3911 64 63 is be AUX iajs-3911 64 64 equal equal ADJ iajs-3911 64 65 to to ADP iajs-3911 64 66 the the DET iajs-3911 64 67 anonymous anonymous ADJ iajs-3911 64 68 parameters parameter NOUN iajs-3911 64 69 . . PUNCT iajs-3911 65 1 the the DET iajs-3911 65 2 posterior posterior ADJ iajs-3911 65 3 density density NOUN iajs-3911 65 4 function function NOUN iajs-3911 65 5 is be AUX iajs-3911 65 6 difficult difficult ADJ iajs-3911 65 7 to to PART iajs-3911 65 8 solve solve VERB iajs-3911 65 9 , , PUNCT iajs-3911 65 10 the the DET iajs-3911 65 11 ratio ratio NOUN iajs-3911 65 12 of of ADP iajs-3911 65 13 these these DET iajs-3911 65 14 integrals integral NOUN iajs-3911 65 15 in in ADP iajs-3911 65 16 equation equation NOUN iajs-3911 65 17 ( ( PUNCT iajs-3911 65 18 15 15 NUM iajs-3911 65 19 ) ) PUNCT iajs-3911 65 20 does do AUX iajs-3911 65 21 not not PART iajs-3911 65 22 seem seem VERB iajs-3911 65 23 to to PART iajs-3911 65 24 take take VERB iajs-3911 65 25 a a DET iajs-3911 65 26 theoretical theoretical ADJ iajs-3911 65 27 formula formula NOUN iajs-3911 65 28 for for ADP iajs-3911 65 29 the the DET iajs-3911 65 30 difficulty difficulty NOUN iajs-3911 65 31 of of ADP iajs-3911 65 32 calculating calculate VERB iajs-3911 65 33 these these DET iajs-3911 65 34 integral integral ADJ iajs-3911 65 35 ( ( PUNCT iajs-3911 65 36 27 27 NUM iajs-3911 65 37 ) ) PUNCT iajs-3911 65 38 . . PUNCT iajs-3911 66 1 then then ADV iajs-3911 66 2 utilizing utilize VERB iajs-3911 66 3 the the DET iajs-3911 66 4 lindely lindely ADJ iajs-3911 66 5 approximation approximation NOUN iajs-3911 66 6 to to PART iajs-3911 66 7 solve solve VERB iajs-3911 66 8 the the DET iajs-3911 66 9 posterior posterior ADJ iajs-3911 66 10 distribution distribution NOUN iajs-3911 66 11 as as SCONJ iajs-3911 66 12 follows follow VERB iajs-3911 66 13 : : PUNCT iajs-3911 66 14 ΞΉ(π‘₯ ΞΉ(π‘₯ NUM iajs-3911 66 15 ) ) PUNCT iajs-3911 67 1 = = SYM iajs-3911 68 1 𝐸(𝑒 𝐸(𝑒 X iajs-3911 68 2 ; ; PUNCT iajs-3911 68 3 𝛼 𝛼 X iajs-3911 68 4 , , PUNCT iajs-3911 68 5 πœ† πœ† X iajs-3911 68 6 ) ) PUNCT iajs-3911 68 7 = = SYM iajs-3911 68 8 ∫ ∫ PROPN iajs-3911 68 9 ∫ ∫ PROPN iajs-3911 68 10 𝑒(𝛼,πœ† 𝑒(𝛼,πœ† NOUN iajs-3911 68 11 ) ) PUNCT iajs-3911 68 12 𝑒𝐿(𝛼,πœ†;𝑑𝑖)+𝐺(𝛼,πœ†)π‘‘π›Όπ‘‘πœ† 𝑒𝐿(𝛼,πœ†;𝑑𝑖)+𝐺(𝛼,πœ†)π‘‘π›Όπ‘‘πœ† VERB iajs-3911 68 13 ∞ ∞ NUM iajs-3911 68 14 0 0 NUM iajs-3911 69 1 ∞ ∞ NUM iajs-3911 69 2 0 0 NUM iajs-3911 70 1 ∫ ∫ PROPN iajs-3911 70 2 ∫ ∫ PROPN iajs-3911 70 3 𝑒𝐿(𝛼,πœ†;𝑑𝑖)+𝐺(𝛼,πœ† 𝑒𝐿(𝛼,πœ†;𝑑𝑖)+𝐺(𝛼,πœ† PROPN iajs-3911 70 4 ) ) PUNCT iajs-3911 71 1 π‘‘π›Όπ‘‘πœ† π‘‘π›Όπ‘‘πœ† VERB iajs-3911 71 2 ∞ ∞ NUM iajs-3911 71 3 0 0 NUM iajs-3911 72 1 ∞ ∞ NUM iajs-3911 72 2 0 0 NUM iajs-3911 72 3 ( ( PUNCT iajs-3911 72 4 17 17 NUM iajs-3911 72 5 ) ) PUNCT iajs-3911 72 6 where where SCONJ iajs-3911 72 7 : : PUNCT iajs-3911 72 8 𝑒(𝛼 𝑒(𝛼 PROPN iajs-3911 72 9 , , PUNCT iajs-3911 72 10 πœ† πœ† NOUN iajs-3911 72 11 ) ) PUNCT iajs-3911 72 12 is be AUX iajs-3911 72 13 function function NOUN iajs-3911 72 14 for for ADP iajs-3911 72 15 𝛼 𝛼 X iajs-3911 72 16 andπœ†. andπœ†. NOUN iajs-3911 73 1 𝐿(𝛼 𝐿(𝛼 NUM iajs-3911 73 2 , , PUNCT iajs-3911 73 3 πœ† πœ† NOUN iajs-3911 73 4 ; ; PUNCT iajs-3911 73 5 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 73 6 ) ) PUNCT iajs-3911 73 7 is be AUX iajs-3911 73 8 natural natural ADJ iajs-3911 73 9 logarithm logarithm NOUN iajs-3911 73 10 of of ADP iajs-3911 73 11 likeihood likeihood NOUN iajs-3911 73 12 function function NOUN iajs-3911 73 13 . . PUNCT iajs-3911 74 1 𝐺(𝛼 𝐺(𝛼 NOUN iajs-3911 74 2 , , PUNCT iajs-3911 74 3 πœ† πœ† X iajs-3911 74 4 ) ) PUNCT iajs-3911 74 5 is be AUX iajs-3911 74 6 natural natural ADJ iajs-3911 74 7 logorithm logorithm ADJ iajs-3911 74 8 of of ADP iajs-3911 74 9 joint joint ADJ iajs-3911 74 10 prior prior ADJ iajs-3911 74 11 density density NOUN iajs-3911 74 12 functions function NOUN iajs-3911 74 13 of of ADP iajs-3911 74 14 𝛼 𝛼 PRON iajs-3911 74 15 and and CCONJ iajs-3911 74 16 πœ†. πœ†. VERB iajs-3911 74 17 then then ADV iajs-3911 74 18 , , PUNCT iajs-3911 74 19 we we PRON iajs-3911 74 20 can can AUX iajs-3911 74 21 calculate calculate VERB iajs-3911 74 22 ΞΉ(π‘₯ ΞΉ(π‘₯ PROPN iajs-3911 74 23 ) ) PUNCT iajs-3911 74 24 = = PUNCT iajs-3911 75 1 𝐸(𝑒 𝐸(𝑒 X iajs-3911 75 2 ; ; PUNCT iajs-3911 75 3 𝛼 𝛼 X iajs-3911 75 4 , , PUNCT iajs-3911 75 5 πœ† πœ† NOUN iajs-3911 75 6 ) ) PUNCT iajs-3911 75 7 as as SCONJ iajs-3911 75 8 follows follow VERB iajs-3911 75 9 : : PUNCT iajs-3911 75 10 ΞΉ(π‘₯ ΞΉ(π‘₯ NUM iajs-3911 75 11 ) ) PUNCT iajs-3911 75 12 = = SYM iajs-3911 75 13 𝑒( 𝑒( NUM iajs-3911 75 14 οΏ½ οΏ½ PROPN iajs-3911 75 15 Μ‚ Μ‚ NUM iajs-3911 75 16 οΏ½ οΏ½ PROPN iajs-3911 75 17 , , PUNCT iajs-3911 75 18 οΏ½ οΏ½ PROPN iajs-3911 75 19 Μ‚ Μ‚ NOUN iajs-3911 75 20 οΏ½ οΏ½ NOUN iajs-3911 75 21 ) ) PUNCT iajs-3911 75 22 + + CCONJ iajs-3911 75 23 1 1 NUM iajs-3911 75 24 2 2 NUM iajs-3911 75 25 [ [ PUNCT iajs-3911 75 26 ( ( PUNCT iajs-3911 75 27 οΏ½ οΏ½ NOUN iajs-3911 75 28 Μ‚ Μ‚ NOUN iajs-3911 75 29 οΏ½ οΏ½ NOUN iajs-3911 75 30 πœ†πœ† πœ†πœ† ADJ iajs-3911 75 31 + + PROPN iajs-3911 75 32 2 2 NUM iajs-3911 75 33 οΏ½ οΏ½ PROPN iajs-3911 75 34 Μ‚ Μ‚ NUM iajs-3911 75 35 οΏ½ οΏ½ PROPN iajs-3911 75 36 πœ† πœ† NOUN iajs-3911 75 37 οΏ½ οΏ½ PROPN iajs-3911 75 38 Μ‚ Μ‚ SYM iajs-3911 75 39 οΏ½ οΏ½ NOUN iajs-3911 75 40 πœ†) πœ†) SYM iajs-3911 75 41 οΏ½ οΏ½ PROPN iajs-3911 75 42 Μ‚ Μ‚ NOUN iajs-3911 75 43 οΏ½ οΏ½ NOUN iajs-3911 75 44 πœ†πœ† πœ†πœ† VERB iajs-3911 75 45 + + CCONJ iajs-3911 75 46 ( ( PUNCT iajs-3911 75 47 οΏ½ οΏ½ PROPN iajs-3911 75 48 Μ‚ Μ‚ VERB iajs-3911 75 49 οΏ½ οΏ½ NOUN iajs-3911 75 50 π›Όπœ† π›Όπœ† VERB iajs-3911 75 51 + + NOUN iajs-3911 75 52 2 2 NUM iajs-3911 75 53 οΏ½ οΏ½ NOUN iajs-3911 75 54 Μ‚ Μ‚ NUM iajs-3911 75 55 οΏ½ οΏ½ NOUN iajs-3911 75 56 𝛼 𝛼 NOUN iajs-3911 75 57 οΏ½ οΏ½ PROPN iajs-3911 75 58 Μ‚ Μ‚ SYM iajs-3911 75 59 οΏ½ οΏ½ NOUN iajs-3911 75 60 πœ†) πœ†) SYM iajs-3911 75 61 οΏ½ οΏ½ PROPN iajs-3911 75 62 Μ‚ Μ‚ VERB iajs-3911 75 63 οΏ½ οΏ½ NOUN iajs-3911 75 64 π›Όπœ† π›Όπœ† VERB iajs-3911 75 65 + + CCONJ iajs-3911 75 66 ( ( PUNCT iajs-3911 75 67 οΏ½ οΏ½ PROPN iajs-3911 75 68 Μ‚ Μ‚ VERB iajs-3911 75 69 οΏ½ οΏ½ NOUN iajs-3911 75 70 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 75 71 + + ADJ iajs-3911 75 72 2 2 NUM iajs-3911 75 73 οΏ½ οΏ½ PROPN iajs-3911 75 74 Μ‚ Μ‚ NUM iajs-3911 75 75 οΏ½ οΏ½ PROPN iajs-3911 75 76 πœ† πœ† NOUN iajs-3911 75 77 οΏ½ οΏ½ PROPN iajs-3911 75 78 Μ‚ Μ‚ VERB iajs-3911 75 79 οΏ½ οΏ½ PROPN iajs-3911 75 80 𝛼) 𝛼) PROPN iajs-3911 75 81 οΏ½ οΏ½ PROPN iajs-3911 75 82 Μ‚ Μ‚ SYM iajs-3911 75 83 οΏ½ οΏ½ NOUN iajs-3911 75 84 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 75 85 + + PROPN iajs-3911 75 86 ( ( PUNCT iajs-3911 75 87 οΏ½ οΏ½ PROPN iajs-3911 75 88 Μ‚ Μ‚ NOUN iajs-3911 75 89 οΏ½ οΏ½ NOUN iajs-3911 75 90 𝛼𝛼 𝛼𝛼 ADP iajs-3911 75 91 + + NOUN iajs-3911 75 92 2 2 NUM iajs-3911 75 93 οΏ½ οΏ½ NOUN iajs-3911 75 94 Μ‚ Μ‚ NUM iajs-3911 75 95 οΏ½ οΏ½ NOUN iajs-3911 75 96 𝛼 𝛼 NOUN iajs-3911 75 97 οΏ½ οΏ½ PROPN iajs-3911 75 98 Μ‚ Μ‚ SYM iajs-3911 75 99 οΏ½ οΏ½ PROPN iajs-3911 75 100 𝛼) 𝛼) PROPN iajs-3911 75 101 οΏ½ οΏ½ PROPN iajs-3911 75 102 Μ‚ Μ‚ NOUN iajs-3911 75 103 οΏ½ οΏ½ NOUN iajs-3911 75 104 𝛼𝛼 𝛼𝛼 ADP iajs-3911 75 105 ] ] PUNCT iajs-3911 75 106 + + CCONJ iajs-3911 75 107 1 1 NUM iajs-3911 75 108 2 2 NUM iajs-3911 75 109 [ [ X iajs-3911 75 110 ( ( PUNCT iajs-3911 75 111 οΏ½ οΏ½ NOUN iajs-3911 75 112 Μ‚ Μ‚ VERB iajs-3911 75 113 οΏ½ οΏ½ PROPN iajs-3911 75 114 πœ† πœ† NOUN iajs-3911 75 115 οΏ½ οΏ½ PROPN iajs-3911 75 116 Μ‚ Μ‚ NOUN iajs-3911 75 117 οΏ½ οΏ½ NOUN iajs-3911 75 118 πœ†πœ† πœ†πœ† ADP iajs-3911 75 119 + + PROPN iajs-3911 75 120 οΏ½ οΏ½ PROPN iajs-3911 75 121 Μ‚ Μ‚ NOUN iajs-3911 75 122 οΏ½ οΏ½ NOUN iajs-3911 75 123 𝛼 𝛼 NOUN iajs-3911 75 124 οΏ½ οΏ½ PROPN iajs-3911 75 125 Μ‚ Μ‚ SYM iajs-3911 75 126 οΏ½ οΏ½ NOUN iajs-3911 75 127 πœ†π›Ό)( πœ†π›Ό)( NOUN iajs-3911 75 128 οΏ½ οΏ½ PROPN iajs-3911 75 129 Μ‚ Μ‚ NOUN iajs-3911 75 130 οΏ½ οΏ½ NOUN iajs-3911 75 131 πœ†πœ†πœ† πœ†πœ†πœ† NOUN iajs-3911 75 132 οΏ½ οΏ½ PROPN iajs-3911 75 133 Μ‚ Μ‚ NOUN iajs-3911 75 134 οΏ½ οΏ½ NOUN iajs-3911 75 135 πœ†πœ† πœ†πœ† ADP iajs-3911 75 136 + + NUM iajs-3911 75 137 οΏ½ οΏ½ PROPN iajs-3911 75 138 Μ‚ Μ‚ SYM iajs-3911 75 139 οΏ½ οΏ½ PROPN iajs-3911 75 140 πœ†π›Όπœ† πœ†π›Όπœ† PROPN iajs-3911 75 141 οΏ½ οΏ½ PROPN iajs-3911 75 142 Μ‚ Μ‚ NOUN iajs-3911 75 143 οΏ½ οΏ½ NOUN iajs-3911 75 144 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 75 145 + + SYM iajs-3911 75 146 οΏ½ οΏ½ PROPN iajs-3911 75 147 Μ‚ Μ‚ NOUN iajs-3911 75 148 οΏ½ οΏ½ PROPN iajs-3911 75 149 π›Όπœ†πœ† π›Όπœ†πœ† ADJ iajs-3911 75 150 οΏ½ οΏ½ PROPN iajs-3911 75 151 Μ‚ Μ‚ VERB iajs-3911 75 152 οΏ½ οΏ½ NOUN iajs-3911 75 153 π›Όπœ† π›Όπœ† SYM iajs-3911 75 154 + + NUM iajs-3911 75 155 οΏ½ οΏ½ PROPN iajs-3911 75 156 Μ‚ Μ‚ SYM iajs-3911 75 157 οΏ½ οΏ½ PROPN iajs-3911 75 158 π›Όπ›Όπœ† π›Όπ›Όπœ† VERB iajs-3911 75 159 οΏ½ οΏ½ PROPN iajs-3911 75 160 Μ‚ Μ‚ NUM iajs-3911 75 161 οΏ½ οΏ½ NOUN iajs-3911 75 162 𝛼𝛼 𝛼𝛼 NOUN iajs-3911 75 163 ) ) PUNCT iajs-3911 75 164 + + CCONJ iajs-3911 75 165 ( ( PUNCT iajs-3911 75 166 οΏ½ οΏ½ PROPN iajs-3911 75 167 Μ‚ Μ‚ VERB iajs-3911 75 168 οΏ½ οΏ½ PROPN iajs-3911 75 169 πœ† πœ† NOUN iajs-3911 75 170 οΏ½ οΏ½ PROPN iajs-3911 75 171 Μ‚ Μ‚ SYM iajs-3911 75 172 οΏ½ οΏ½ NOUN iajs-3911 75 173 π›Όπœ† π›Όπœ† SYM iajs-3911 75 174 + + NUM iajs-3911 75 175 οΏ½ οΏ½ PROPN iajs-3911 75 176 Μ‚ Μ‚ NOUN iajs-3911 75 177 οΏ½ οΏ½ NOUN iajs-3911 75 178 𝛼 𝛼 NOUN iajs-3911 75 179 οΏ½ οΏ½ PROPN iajs-3911 75 180 Μ‚ Μ‚ SYM iajs-3911 75 181 οΏ½ οΏ½ NOUN iajs-3911 75 182 𝛼𝛼)( 𝛼𝛼)( NOUN iajs-3911 75 183 οΏ½ οΏ½ PROPN iajs-3911 75 184 Μ‚ Μ‚ NOUN iajs-3911 75 185 οΏ½ οΏ½ PROPN iajs-3911 75 186 π›Όπœ†πœ† π›Όπœ†πœ† ADJ iajs-3911 75 187 οΏ½ οΏ½ PROPN iajs-3911 75 188 Μ‚ Μ‚ NOUN iajs-3911 75 189 οΏ½ οΏ½ NOUN iajs-3911 75 190 πœ†πœ† πœ†πœ† ADP iajs-3911 75 191 + + NUM iajs-3911 75 192 οΏ½ οΏ½ PROPN iajs-3911 75 193 Μ‚ Μ‚ NOUN iajs-3911 75 194 οΏ½ οΏ½ PROPN iajs-3911 75 195 πœ†π›Όπ›Ό πœ†π›Όπ›Ό NOUN iajs-3911 75 196 οΏ½ οΏ½ PROPN iajs-3911 75 197 Μ‚ Μ‚ VERB iajs-3911 75 198 οΏ½ οΏ½ NOUN iajs-3911 75 199 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 75 200 + + SYM iajs-3911 75 201 οΏ½ οΏ½ PROPN iajs-3911 75 202 Μ‚ Μ‚ NOUN iajs-3911 75 203 οΏ½ οΏ½ PROPN iajs-3911 75 204 π›Όπœ†π›Ό π›Όπœ†π›Ό NOUN iajs-3911 75 205 οΏ½ οΏ½ PROPN iajs-3911 75 206 Μ‚ Μ‚ VERB iajs-3911 75 207 οΏ½ οΏ½ NOUN iajs-3911 75 208 π›Όπœ† π›Όπœ† SYM iajs-3911 75 209 + + NUM iajs-3911 75 210 οΏ½ οΏ½ PROPN iajs-3911 75 211 Μ‚ Μ‚ NUM iajs-3911 75 212 οΏ½ οΏ½ NOUN iajs-3911 75 213 𝛼𝛼𝛼 𝛼𝛼𝛼 VERB iajs-3911 75 214 οΏ½ οΏ½ PROPN iajs-3911 75 215 Μ‚ Μ‚ PROPN iajs-3911 75 216 οΏ½ οΏ½ NOUN iajs-3911 75 217 𝛼𝛼 𝛼𝛼 NOUN iajs-3911 75 218 ) ) PUNCT iajs-3911 75 219 ] ] PUNCT iajs-3911 75 220 ( ( PUNCT iajs-3911 75 221 18 18 NUM iajs-3911 75 222 ) ) PUNCT iajs-3911 75 223 then then ADV iajs-3911 75 224 applying apply VERB iajs-3911 75 225 the the DET iajs-3911 75 226 lindely lindely ADJ iajs-3911 75 227 approach approach NOUN iajs-3911 75 228 as as ADP iajs-3911 75 229 in in ADP iajs-3911 75 230 equation equation NOUN iajs-3911 75 231 ( ( PUNCT iajs-3911 75 232 5 5 X iajs-3911 75 233 ) ) PUNCT iajs-3911 75 234 we we PRON iajs-3911 75 235 get get VERB iajs-3911 75 236 : : PUNCT iajs-3911 75 237 𝑒( 𝑒( NUM iajs-3911 75 238 οΏ½ οΏ½ PROPN iajs-3911 75 239 Μ‚ Μ‚ NUM iajs-3911 75 240 οΏ½ οΏ½ PROPN iajs-3911 75 241 , , PUNCT iajs-3911 75 242 οΏ½ οΏ½ PROPN iajs-3911 75 243 Μ‚ Μ‚ NOUN iajs-3911 75 244 οΏ½ οΏ½ NOUN iajs-3911 75 245 ) ) PUNCT iajs-3911 75 246 = = SYM iajs-3911 75 247 𝛼 𝛼 X iajs-3911 75 248 , , PUNCT iajs-3911 75 249 οΏ½ οΏ½ NOUN iajs-3911 75 250 Μ‚ Μ‚ NOUN iajs-3911 75 251 οΏ½ οΏ½ NOUN iajs-3911 75 252 𝛼 𝛼 NOUN iajs-3911 75 253 = = PROPN iajs-3911 75 254 πœ•π‘’( πœ•π‘’( PROPN iajs-3911 75 255 οΏ½ οΏ½ PROPN iajs-3911 75 256 Μ‚ Μ‚ VERB iajs-3911 75 257 οΏ½ οΏ½ PROPN iajs-3911 75 258 , , PUNCT iajs-3911 75 259 οΏ½ οΏ½ PROPN iajs-3911 75 260 Μ‚ Μ‚ NOUN iajs-3911 75 261 οΏ½ οΏ½ NOUN iajs-3911 75 262 ) ) PUNCT iajs-3911 75 263 πœ•π›Ό πœ•π›Ό NOUN iajs-3911 75 264 = = SYM iajs-3911 75 265 1 1 NUM iajs-3911 75 266 , , PUNCT iajs-3911 75 267 οΏ½ οΏ½ NOUN iajs-3911 75 268 Μ‚ Μ‚ NOUN iajs-3911 75 269 οΏ½ οΏ½ NOUN iajs-3911 75 270 𝛼𝛼 𝛼𝛼 ADP iajs-3911 75 271 = = SYM iajs-3911 75 272 0 0 NUM iajs-3911 75 273 , , PUNCT iajs-3911 75 274 οΏ½ οΏ½ NOUN iajs-3911 75 275 Μ‚ Μ‚ NOUN iajs-3911 75 276 οΏ½ οΏ½ PROPN iajs-3911 75 277 πœ† πœ† NOUN iajs-3911 75 278 = = SYM iajs-3911 75 279 0 0 NUM iajs-3911 75 280 , , PUNCT iajs-3911 75 281 οΏ½ οΏ½ NOUN iajs-3911 75 282 Μ‚ Μ‚ NOUN iajs-3911 75 283 οΏ½ οΏ½ NOUN iajs-3911 75 284 πœ†πœ† πœ†πœ† NOUN iajs-3911 75 285 = = SYM iajs-3911 75 286 0 0 NUM iajs-3911 75 287 , , PUNCT iajs-3911 75 288 οΏ½ οΏ½ NOUN iajs-3911 75 289 Μ‚ Μ‚ NOUN iajs-3911 75 290 οΏ½ οΏ½ NOUN iajs-3911 75 291 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 75 292 = = SYM iajs-3911 75 293 0 0 NUM iajs-3911 75 294 , , PUNCT iajs-3911 75 295 οΏ½ οΏ½ NOUN iajs-3911 75 296 Μ‚ Μ‚ VERB iajs-3911 75 297 οΏ½ οΏ½ NOUN iajs-3911 75 298 π›Όπœ† π›Όπœ† X iajs-3911 75 299 = = SYM iajs-3911 75 300 0 0 NUM iajs-3911 75 301 ΞΉ(π‘₯ ΞΉ(π‘₯ NOUN iajs-3911 75 302 ) ) PUNCT iajs-3911 75 303 = = SYM iajs-3911 75 304 οΏ½ οΏ½ PROPN iajs-3911 75 305 Μ‚ Μ‚ NUM iajs-3911 75 306 οΏ½ οΏ½ NOUN iajs-3911 75 307 + + CCONJ iajs-3911 75 308 1 1 NUM iajs-3911 75 309 2 2 NUM iajs-3911 75 310 [ [ X iajs-3911 75 311 ( ( PUNCT iajs-3911 75 312 2 2 NUM iajs-3911 75 313 οΏ½ οΏ½ NOUN iajs-3911 75 314 Μ‚ Μ‚ VERB iajs-3911 75 315 οΏ½ οΏ½ NOUN iajs-3911 75 316 πœ†) πœ†) SYM iajs-3911 75 317 οΏ½ οΏ½ PROPN iajs-3911 75 318 Μ‚ Μ‚ VERB iajs-3911 75 319 οΏ½ οΏ½ NOUN iajs-3911 75 320 π›Όπœ† π›Όπœ† VERB iajs-3911 75 321 + + CCONJ iajs-3911 75 322 ( ( PUNCT iajs-3911 75 323 2 2 NUM iajs-3911 75 324 οΏ½ οΏ½ NOUN iajs-3911 75 325 Μ‚ Μ‚ VERB iajs-3911 75 326 οΏ½ οΏ½ NOUN iajs-3911 75 327 𝛼) 𝛼) PROPN iajs-3911 75 328 οΏ½ οΏ½ PROPN iajs-3911 75 329 Μ‚ Μ‚ NOUN iajs-3911 75 330 οΏ½ οΏ½ NOUN iajs-3911 75 331 𝛼𝛼 𝛼𝛼 ADP iajs-3911 75 332 ] ] X iajs-3911 75 333 + + CCONJ iajs-3911 75 334 1 1 NUM iajs-3911 75 335 2 2 NUM iajs-3911 75 336 [ [ X iajs-3911 75 337 ( ( PUNCT iajs-3911 75 338 οΏ½ οΏ½ NOUN iajs-3911 75 339 Μ‚ Μ‚ NOUN iajs-3911 75 340 οΏ½ οΏ½ PROPN iajs-3911 75 341 πœ†π›Ό)( πœ†π›Ό)( NOUN iajs-3911 75 342 οΏ½ οΏ½ PROPN iajs-3911 75 343 Μ‚ Μ‚ NOUN iajs-3911 75 344 οΏ½ οΏ½ NOUN iajs-3911 75 345 πœ†πœ†πœ† πœ†πœ†πœ† NOUN iajs-3911 75 346 οΏ½ οΏ½ PROPN iajs-3911 75 347 Μ‚ Μ‚ NOUN iajs-3911 75 348 οΏ½ οΏ½ NOUN iajs-3911 75 349 πœ†πœ† πœ†πœ† ADP iajs-3911 75 350 + + NUM iajs-3911 75 351 οΏ½ οΏ½ PROPN iajs-3911 75 352 Μ‚ Μ‚ SYM iajs-3911 75 353 οΏ½ οΏ½ PROPN iajs-3911 75 354 πœ†π›Όπœ† πœ†π›Όπœ† PROPN iajs-3911 75 355 οΏ½ οΏ½ PROPN iajs-3911 75 356 Μ‚ Μ‚ NOUN iajs-3911 75 357 οΏ½ οΏ½ NOUN iajs-3911 75 358 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 75 359 + + SYM iajs-3911 75 360 οΏ½ οΏ½ PROPN iajs-3911 75 361 Μ‚ Μ‚ NOUN iajs-3911 75 362 οΏ½ οΏ½ PROPN iajs-3911 75 363 π›Όπœ†πœ† π›Όπœ†πœ† ADJ iajs-3911 75 364 οΏ½ οΏ½ PROPN iajs-3911 75 365 Μ‚ Μ‚ VERB iajs-3911 75 366 οΏ½ οΏ½ NOUN iajs-3911 75 367 π›Όπœ† π›Όπœ† SYM iajs-3911 75 368 + + NUM iajs-3911 75 369 οΏ½ οΏ½ PROPN iajs-3911 75 370 Μ‚ Μ‚ SYM iajs-3911 75 371 οΏ½ οΏ½ PROPN iajs-3911 75 372 π›Όπ›Όπœ† π›Όπ›Όπœ† VERB iajs-3911 75 373 οΏ½ οΏ½ PROPN iajs-3911 75 374 Μ‚ Μ‚ NUM iajs-3911 75 375 οΏ½ οΏ½ NOUN iajs-3911 75 376 𝛼𝛼 𝛼𝛼 NOUN iajs-3911 75 377 ) ) PUNCT iajs-3911 75 378 + + PROPN iajs-3911 75 379 ( ( PUNCT iajs-3911 75 380 οΏ½ οΏ½ NOUN iajs-3911 75 381 Μ‚ Μ‚ SYM iajs-3911 75 382 οΏ½ οΏ½ PROPN iajs-3911 75 383 𝛼𝛼)( 𝛼𝛼)( NOUN iajs-3911 75 384 οΏ½ οΏ½ PROPN iajs-3911 75 385 Μ‚ Μ‚ NOUN iajs-3911 75 386 οΏ½ οΏ½ PROPN iajs-3911 75 387 π›Όπœ†πœ† π›Όπœ†πœ† ADJ iajs-3911 75 388 οΏ½ οΏ½ PROPN iajs-3911 75 389 Μ‚ Μ‚ NOUN iajs-3911 75 390 οΏ½ οΏ½ NOUN iajs-3911 75 391 πœ†πœ† πœ†πœ† ADP iajs-3911 75 392 + + NUM iajs-3911 75 393 οΏ½ οΏ½ PROPN iajs-3911 75 394 Μ‚ Μ‚ NOUN iajs-3911 75 395 οΏ½ οΏ½ PROPN iajs-3911 75 396 πœ†π›Όπ›Ό πœ†π›Όπ›Ό NOUN iajs-3911 75 397 οΏ½ οΏ½ PROPN iajs-3911 75 398 Μ‚ Μ‚ VERB iajs-3911 75 399 οΏ½ οΏ½ NOUN iajs-3911 75 400 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 75 401 + + SYM iajs-3911 75 402 οΏ½ οΏ½ PROPN iajs-3911 75 403 Μ‚ Μ‚ NOUN iajs-3911 75 404 οΏ½ οΏ½ PROPN iajs-3911 75 405 π›Όπœ†π›Ό π›Όπœ†π›Ό NOUN iajs-3911 75 406 οΏ½ οΏ½ PROPN iajs-3911 75 407 Μ‚ Μ‚ VERB iajs-3911 75 408 οΏ½ οΏ½ NOUN iajs-3911 75 409 π›Όπœ† π›Όπœ† SYM iajs-3911 75 410 + + NUM iajs-3911 75 411 οΏ½ οΏ½ PROPN iajs-3911 75 412 Μ‚ Μ‚ NUM iajs-3911 75 413 οΏ½ οΏ½ NOUN iajs-3911 75 414 𝛼𝛼𝛼 𝛼𝛼𝛼 VERB iajs-3911 75 415 οΏ½ οΏ½ PROPN iajs-3911 75 416 Μ‚ Μ‚ PROPN iajs-3911 75 417 οΏ½ οΏ½ NOUN iajs-3911 75 418 𝛼𝛼 𝛼𝛼 NOUN iajs-3911 75 419 ) ) PUNCT iajs-3911 75 420 ] ] PUNCT iajs-3911 75 421 ( ( PUNCT iajs-3911 75 422 19 19 NUM iajs-3911 75 423 ) ) PUNCT iajs-3911 75 424 now now ADV iajs-3911 75 425 derivate derivate VERB iajs-3911 75 426 𝑃 𝑃 NOUN iajs-3911 75 427 = = PUNCT iajs-3911 75 428 ln ln ADJ iajs-3911 75 429 𝑔(𝛼 𝑔(𝛼 PROPN iajs-3911 75 430 , , PUNCT iajs-3911 75 431 πœ† πœ† NOUN iajs-3911 75 432 ) ) PUNCT iajs-3911 75 433 with with ADP iajs-3911 75 434 respect respect NOUN iajs-3911 75 435 to to ADP iajs-3911 75 436 𝛼 𝛼 PRON iajs-3911 75 437 and and CCONJ iajs-3911 75 438 πœ† πœ† ADP iajs-3911 75 439 in in ADP iajs-3911 75 440 equation equation NOUN iajs-3911 75 441 ( ( PUNCT iajs-3911 75 442 11 11 NUM iajs-3911 75 443 ) ) PUNCT iajs-3911 75 444 we we PRON iajs-3911 75 445 get get VERB iajs-3911 75 446 : : PUNCT iajs-3911 75 447 οΏ½ οΏ½ PROPN iajs-3911 75 448 Μ‚ Μ‚ NOUN iajs-3911 75 449 οΏ½ οΏ½ PROPN iajs-3911 75 450 πœ† πœ† NOUN iajs-3911 76 1 = = PUNCT iajs-3911 77 1 πœ• πœ• PROPN iajs-3911 77 2 𝑙𝑛 𝑙𝑛 NOUN iajs-3911 77 3 𝑔(𝛼,πœ† 𝑔(𝛼,πœ† NOUN iajs-3911 77 4 ) ) PUNCT iajs-3911 77 5 πœ•πœ† πœ•πœ† NOUN iajs-3911 77 6 = = PUNCT iajs-3911 77 7 βˆ’πœƒ βˆ’πœƒ NOUN iajs-3911 77 8 , , PUNCT iajs-3911 77 9 οΏ½ οΏ½ PROPN iajs-3911 77 10 Μ‚ Μ‚ NOUN iajs-3911 77 11 οΏ½ οΏ½ NOUN iajs-3911 77 12 𝛼 𝛼 NOUN iajs-3911 77 13 = = NOUN iajs-3911 77 14 πœ• πœ• PROPN iajs-3911 77 15 𝑙𝑛 𝑙𝑛 NOUN iajs-3911 77 16 𝑔(𝛼,πœ† 𝑔(𝛼,πœ† NOUN iajs-3911 77 17 ) ) PUNCT iajs-3911 77 18 πœ•π›Ό πœ•π›Ό NOUN iajs-3911 77 19 = = SYM iajs-3911 77 20 βˆ’πœƒ βˆ’πœƒ NOUN iajs-3911 77 21 , , PUNCT iajs-3911 77 22 οΏ½ οΏ½ PROPN iajs-3911 77 23 Μ‚ Μ‚ NOUN iajs-3911 77 24 οΏ½ οΏ½ NOUN iajs-3911 77 25 𝛼 𝛼 NOUN iajs-3911 77 26 = = SYM iajs-3911 77 27 πœ• πœ• PROPN iajs-3911 77 28 ln𝐿 ln𝐿 PROPN iajs-3911 77 29 πœ•π›Ό πœ•π›Ό NOUN iajs-3911 77 30 = = PUNCT iajs-3911 77 31 βˆ‘ βˆ‘ PUNCT iajs-3911 77 32 1 1 NUM iajs-3911 77 33 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 34 βˆ’π‘› βˆ’π‘› VERB iajs-3911 77 35 𝑖=1 𝑖=1 PROPN iajs-3911 77 36 βˆ‘ βˆ‘ PROPN iajs-3911 77 37 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 38 𝑛 𝑛 PRON iajs-3911 77 39 𝑖=1 𝑖=1 PROPN iajs-3911 77 40 οΏ½ οΏ½ PROPN iajs-3911 77 41 Μ‚ Μ‚ NOUN iajs-3911 77 42 οΏ½ οΏ½ PROPN iajs-3911 77 43 πœ† πœ† DET iajs-3911 77 44 = = SYM iajs-3911 77 45 πœ• πœ• PROPN iajs-3911 77 46 ln𝐿 ln𝐿 NOUN iajs-3911 77 47 πœ•πœ† πœ•πœ† NOUN iajs-3911 77 48 = = PUNCT iajs-3911 77 49 βˆ‘ βˆ‘ PROPN iajs-3911 77 50 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 51 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– PRON iajs-3911 77 52 βˆ’ βˆ’ PROPN iajs-3911 77 53 βˆ‘ βˆ‘ PROPN iajs-3911 77 54 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 55 2𝑛 2𝑛 PROPN iajs-3911 77 56 𝑖=1 𝑖=1 PROPN iajs-3911 77 57 2 2 NUM iajs-3911 77 58 𝑛 𝑛 PRON iajs-3911 77 59 𝑖=1 𝑖=1 PROPN iajs-3911 77 60 , , PUNCT iajs-3911 77 61 οΏ½ οΏ½ PROPN iajs-3911 77 62 Μ‚ Μ‚ NOUN iajs-3911 77 63 οΏ½ οΏ½ NOUN iajs-3911 77 64 πœ†πœ† πœ†πœ† NOUN iajs-3911 77 65 = = SYM iajs-3911 77 66 πœ•2 πœ•2 NOUN iajs-3911 77 67 ln𝐿 ln𝐿 PROPN iajs-3911 77 68 πœ•πœ†2 πœ•πœ†2 PROPN iajs-3911 77 69 = = SYM iajs-3911 77 70 βˆ’βˆ‘ βˆ’βˆ‘ PROPN iajs-3911 77 71 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 72 2 2 NUM iajs-3911 77 73 ( ( PUNCT iajs-3911 77 74 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 75 ) ) PUNCT iajs-3911 77 76 2 2 NUM iajs-3911 77 77 𝑛 𝑛 PRON iajs-3911 77 78 𝑖=1 𝑖=1 PROPN iajs-3911 77 79 , , PUNCT iajs-3911 77 80 οΏ½ οΏ½ PROPN iajs-3911 77 81 Μ‚ Μ‚ NOUN iajs-3911 77 82 οΏ½ οΏ½ NOUN iajs-3911 77 83 𝛼𝛼 𝛼𝛼 NOUN iajs-3911 77 84 = = SYM iajs-3911 77 85 πœ•2 πœ•2 NOUN iajs-3911 77 86 ln ln PROPN iajs-3911 77 87 𝐿 𝐿 PROPN iajs-3911 77 88 πœ•π›Ό2 πœ•π›Ό2 NOUN iajs-3911 77 89 = = SYM iajs-3911 77 90 βˆ’βˆ‘ βˆ’βˆ‘ PROPN iajs-3911 77 91 1 1 NUM iajs-3911 77 92 ( ( PUNCT iajs-3911 77 93 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 94 ) ) PUNCT iajs-3911 77 95 2 2 NUM iajs-3911 77 96 𝑛 𝑛 PRON iajs-3911 77 97 𝑖=1 𝑖=1 PROPN iajs-3911 77 98 , , PUNCT iajs-3911 77 99 οΏ½ οΏ½ PROPN iajs-3911 77 100 Μ‚ Μ‚ VERB iajs-3911 77 101 οΏ½ οΏ½ NOUN iajs-3911 77 102 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 77 103 = = SYM iajs-3911 77 104 πœ•2 πœ•2 NOUN iajs-3911 77 105 ln ln PROPN iajs-3911 77 106 𝐿 𝐿 PROPN iajs-3911 77 107 πœ•πœ†πœ•π›Ό πœ•πœ†πœ•π›Ό X iajs-3911 77 108 = = SYM iajs-3911 77 109 βˆ’βˆ‘ βˆ’βˆ‘ PROPN iajs-3911 77 110 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 111 ( ( PUNCT iajs-3911 77 112 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 113 ) ) PUNCT iajs-3911 77 114 2 2 NUM iajs-3911 77 115 𝑛 𝑛 PRON iajs-3911 77 116 𝑖=1 𝑖=1 PROPN iajs-3911 77 117 , , PUNCT iajs-3911 77 118 οΏ½ οΏ½ PROPN iajs-3911 77 119 Μ‚ Μ‚ VERB iajs-3911 77 120 οΏ½ οΏ½ NOUN iajs-3911 77 121 π›Όπœ† π›Όπœ† VERB iajs-3911 77 122 = = SYM iajs-3911 77 123 πœ•2 πœ•2 NOUN iajs-3911 77 124 ln ln PROPN iajs-3911 77 125 𝐿 𝐿 PROPN iajs-3911 77 126 πœ•π›Όπœ•πœ† πœ•π›Όπœ•πœ† PROPN iajs-3911 77 127 = = SYM iajs-3911 77 128 βˆ’βˆ‘ βˆ’βˆ‘ PROPN iajs-3911 77 129 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 130 ( ( PUNCT iajs-3911 77 131 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 132 ) ) PUNCT iajs-3911 77 133 2 2 NUM iajs-3911 77 134 𝑛 𝑛 PRON iajs-3911 77 135 𝑖=1 𝑖=1 PROPN iajs-3911 77 136 , , PUNCT iajs-3911 77 137 οΏ½ οΏ½ PROPN iajs-3911 77 138 Μ‚ Μ‚ NOUN iajs-3911 77 139 οΏ½ οΏ½ NOUN iajs-3911 77 140 πœ†πœ†π›Ό πœ†πœ†π›Ό VERB iajs-3911 77 141 = = SYM iajs-3911 77 142 πœ•3 πœ•3 NOUN iajs-3911 77 143 ln𝐿 ln𝐿 PROPN iajs-3911 77 144 πœ•πœ†2πœ•π›Ό πœ•πœ†2πœ•π›Ό NOUN iajs-3911 77 145 = = PROPN iajs-3911 77 146 2βˆ‘ 2βˆ‘ PROPN iajs-3911 77 147 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 148 2 2 NUM iajs-3911 77 149 ( ( PUNCT iajs-3911 77 150 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 151 ) ) PUNCT iajs-3911 77 152 3 3 NUM iajs-3911 77 153 𝑛 𝑛 PRON iajs-3911 77 154 𝑖=1 𝑖=1 PROPN iajs-3911 77 155 οΏ½ οΏ½ PROPN iajs-3911 77 156 Μ‚ Μ‚ NOUN iajs-3911 77 157 οΏ½ οΏ½ NOUN iajs-3911 77 158 πœ†πœ†πœ† πœ†πœ†πœ† NOUN iajs-3911 77 159 = = SYM iajs-3911 77 160 πœ•3 πœ•3 NOUN iajs-3911 77 161 ln ln ADJ iajs-3911 77 162 𝐿 𝐿 PROPN iajs-3911 77 163 πœ•πœ†3 πœ•πœ†3 NOUN iajs-3911 77 164 = = SYM iajs-3911 77 165 2βˆ‘ 2βˆ‘ NUM iajs-3911 77 166 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 167 3 3 NUM iajs-3911 77 168 ( ( PUNCT iajs-3911 77 169 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 170 ) ) PUNCT iajs-3911 77 171 3 3 NUM iajs-3911 77 172 𝑛 𝑛 PROPN iajs-3911 77 173 𝑖=1 𝑖=1 PROPN iajs-3911 77 174 , , PUNCT iajs-3911 77 175 οΏ½ οΏ½ PROPN iajs-3911 77 176 Μ‚ Μ‚ VERB iajs-3911 77 177 οΏ½ οΏ½ NOUN iajs-3911 77 178 πœ†π›Όπœ† πœ†π›Όπœ† NOUN iajs-3911 77 179 = = SYM iajs-3911 77 180 πœ•3 πœ•3 NOUN iajs-3911 77 181 ln ln ADJ iajs-3911 77 182 𝐿 𝐿 NOUN iajs-3911 77 183 πœ•πœ†πœ•π›Όπœ•πœ† πœ•πœ†πœ•π›Όπœ•πœ† PROPN iajs-3911 77 184 = = SYM iajs-3911 77 185 2βˆ‘ 2βˆ‘ NUM iajs-3911 77 186 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 187 2 2 NUM iajs-3911 77 188 ( ( PUNCT iajs-3911 77 189 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 190 ) ) PUNCT iajs-3911 77 191 3 3 NUM iajs-3911 77 192 𝑛 𝑛 PRON iajs-3911 77 193 𝑖=1 𝑖=1 PROPN iajs-3911 77 194 οΏ½ οΏ½ PROPN iajs-3911 77 195 Μ‚ Μ‚ VERB iajs-3911 77 196 οΏ½ οΏ½ NOUN iajs-3911 77 197 π›Όπ›Όπœ† π›Όπ›Όπœ† VERB iajs-3911 77 198 = = PUNCT iajs-3911 77 199 πœ•3 πœ•3 NOUN iajs-3911 77 200 ln ln PROPN iajs-3911 77 201 𝐿 𝐿 PROPN iajs-3911 77 202 πœ•π›Όπœ•π›Όπœ•πœ† πœ•π›Όπœ•π›Όπœ•πœ† PROPN iajs-3911 77 203 = = SYM iajs-3911 77 204 2βˆ‘ 2βˆ‘ NUM iajs-3911 77 205 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 206 ( ( PUNCT iajs-3911 77 207 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 208 ) ) PUNCT iajs-3911 77 209 3 3 NUM iajs-3911 77 210 𝑛 𝑛 PROPN iajs-3911 77 211 𝑖=1 𝑖=1 PROPN iajs-3911 77 212 , , PUNCT iajs-3911 77 213 οΏ½ οΏ½ PROPN iajs-3911 77 214 Μ‚ Μ‚ NOUN iajs-3911 77 215 οΏ½ οΏ½ NOUN iajs-3911 77 216 π›Όπœ†πœ† π›Όπœ†πœ† NOUN iajs-3911 77 217 = = SYM iajs-3911 77 218 πœ•3 πœ•3 NOUN iajs-3911 77 219 ln ln ADJ iajs-3911 77 220 𝐿 𝐿 NOUN iajs-3911 77 221 πœ•π›Όπœ•πœ†πœ•πœ† πœ•π›Όπœ•πœ†πœ•πœ† NOUN iajs-3911 77 222 = = SYM iajs-3911 77 223 2βˆ‘ 2βˆ‘ NUM iajs-3911 77 224 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 225 2 2 NUM iajs-3911 77 226 ( ( PUNCT iajs-3911 77 227 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 228 ) ) PUNCT iajs-3911 77 229 3 3 NUM iajs-3911 77 230 𝑛 𝑛 PRON iajs-3911 77 231 𝑖=1 𝑖=1 PROPN iajs-3911 77 232 οΏ½ οΏ½ PROPN iajs-3911 77 233 Μ‚ Μ‚ NOUN iajs-3911 77 234 οΏ½ οΏ½ PROPN iajs-3911 77 235 πœ†π›Όπ›Ό πœ†π›Όπ›Ό NOUN iajs-3911 77 236 = = SYM iajs-3911 77 237 πœ•3 πœ•3 NOUN iajs-3911 77 238 ln ln PROPN iajs-3911 77 239 𝐿 𝐿 PROPN iajs-3911 77 240 πœ•πœ†πœ•π›Όπœ•π›Ό πœ•πœ†πœ•π›Όπœ•π›Ό PROPN iajs-3911 77 241 = = SYM iajs-3911 77 242 2βˆ‘ 2βˆ‘ NUM iajs-3911 77 243 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 77 244 ( ( PUNCT iajs-3911 77 245 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 77 246 ) ) PUNCT iajs-3911 77 247 3 3 NUM iajs-3911 77 248 𝑛 𝑛 PROPN iajs-3911 77 249 𝑖=1 𝑖=1 PROPN iajs-3911 77 250 , , PUNCT iajs-3911 77 251 οΏ½ οΏ½ PROPN iajs-3911 77 252 Μ‚ Μ‚ VERB iajs-3911 77 253 οΏ½ οΏ½ NOUN iajs-3911 77 254 𝛼𝛼𝛼 𝛼𝛼𝛼 NOUN iajs-3911 77 255 = = SYM iajs-3911 77 256 πœ•3 πœ•3 PROPN iajs-3911 77 257 ln ln ADJ iajs-3911 77 258 𝐿 𝐿 PROPN iajs-3911 77 259 πœ•π›Ό3 πœ•π›Ό3 NOUN iajs-3911 77 260 = = PUNCT iajs-3911 78 1 2βˆ‘ 2βˆ‘ NUM iajs-3911 78 2 1 1 NUM iajs-3911 78 3 ( ( PUNCT iajs-3911 78 4 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 78 5 ) ) PUNCT iajs-3911 78 6 3 3 NUM iajs-3911 78 7 𝑛 𝑛 PRON iajs-3911 78 8 𝑖=1 𝑖=1 PROPN iajs-3911 78 9 οΏ½ οΏ½ PROPN iajs-3911 78 10 Μ‚ Μ‚ NOUN iajs-3911 78 11 οΏ½ οΏ½ NOUN iajs-3911 78 12 π›Όπœ†π›Ό π›Όπœ†π›Ό NOUN iajs-3911 78 13 = = SYM iajs-3911 78 14 πœ•3 πœ•3 NOUN iajs-3911 78 15 ln𝐿 ln𝐿 NOUN iajs-3911 78 16 πœ•π›Όπœ•πœ†πœ•π›Ό πœ•π›Όπœ•πœ†πœ•π›Ό NUM iajs-3911 78 17 = = SYM iajs-3911 78 18 2βˆ‘ 2βˆ‘ NUM iajs-3911 78 19 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 78 20 ( ( PUNCT iajs-3911 78 21 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 78 22 ) ) PUNCT iajs-3911 78 23 3 3 NUM iajs-3911 78 24 𝑛 𝑛 PROPN iajs-3911 78 25 𝑖=1 𝑖=1 PROPN iajs-3911 78 26 , , PUNCT iajs-3911 78 27 οΏ½ οΏ½ PROPN iajs-3911 78 28 Μ‚ Μ‚ VERB iajs-3911 78 29 οΏ½ οΏ½ NOUN iajs-3911 78 30 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 78 31 = = SYM iajs-3911 78 32 βˆ’ βˆ’ PROPN iajs-3911 78 33 1 1 NUM iajs-3911 78 34 οΏ½ οΏ½ PROPN iajs-3911 78 35 Μ‚ Μ‚ NUM iajs-3911 78 36 οΏ½ οΏ½ NOUN iajs-3911 78 37 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 78 38 = = SYM iajs-3911 78 39 1 1 NUM iajs-3911 78 40 βˆ‘ βˆ‘ PROPN iajs-3911 78 41 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 78 42 ( ( PUNCT iajs-3911 78 43 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 78 44 ) ) PUNCT iajs-3911 78 45 2 2 NUM iajs-3911 78 46 𝑛 𝑛 PRON iajs-3911 78 47 𝑖=1 𝑖=1 PROPN iajs-3911 78 48 οΏ½ οΏ½ PROPN iajs-3911 78 49 Μ‚ Μ‚ NOUN iajs-3911 78 50 οΏ½ οΏ½ NOUN iajs-3911 78 51 𝛼𝛼 𝛼𝛼 ADP iajs-3911 78 52 = = SYM iajs-3911 78 53 βˆ’ βˆ’ PROPN iajs-3911 78 54 1 1 NUM iajs-3911 78 55 οΏ½ οΏ½ PROPN iajs-3911 78 56 Μ‚ Μ‚ NOUN iajs-3911 78 57 οΏ½ οΏ½ NOUN iajs-3911 78 58 𝛼𝛼 𝛼𝛼 ADP iajs-3911 78 59 = = SYM iajs-3911 78 60 1 1 NUM iajs-3911 78 61 βˆ‘ βˆ‘ SYM iajs-3911 78 62 1 1 NUM iajs-3911 78 63 ( ( PUNCT iajs-3911 78 64 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 78 65 ) ) PUNCT iajs-3911 78 66 2 2 NUM iajs-3911 78 67 𝑛 𝑛 PRON iajs-3911 78 68 𝑖=1 𝑖=1 PROPN iajs-3911 78 69 , , PUNCT iajs-3911 78 70 οΏ½ οΏ½ PROPN iajs-3911 78 71 Μ‚ Μ‚ NOUN iajs-3911 78 72 οΏ½ οΏ½ NOUN iajs-3911 78 73 πœ†πœ† πœ†πœ† NOUN iajs-3911 78 74 = = SYM iajs-3911 78 75 βˆ’ βˆ’ PROPN iajs-3911 78 76 1 1 NUM iajs-3911 78 77 οΏ½ οΏ½ PROPN iajs-3911 78 78 Μ‚ Μ‚ NOUN iajs-3911 78 79 οΏ½ οΏ½ NOUN iajs-3911 78 80 πœ†πœ† πœ†πœ† NOUN iajs-3911 78 81 = = SYM iajs-3911 78 82 1 1 NUM iajs-3911 78 83 βˆ‘ βˆ‘ NOUN iajs-3911 78 84 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 78 85 2 2 NUM iajs-3911 78 86 ( ( PUNCT iajs-3911 78 87 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 78 88 ) ) PUNCT iajs-3911 78 89 2 2 NUM iajs-3911 78 90 𝑛 𝑛 PRON iajs-3911 78 91 𝑖=1 𝑖=1 PROPN iajs-3911 78 92 , , PUNCT iajs-3911 78 93 οΏ½ οΏ½ PROPN iajs-3911 78 94 Μ‚ Μ‚ VERB iajs-3911 78 95 οΏ½ οΏ½ NOUN iajs-3911 78 96 π›Όπœ† π›Όπœ† X iajs-3911 78 97 = = SYM iajs-3911 78 98 βˆ’ βˆ’ PROPN iajs-3911 78 99 1 1 NUM iajs-3911 78 100 οΏ½ οΏ½ PROPN iajs-3911 78 101 Μ‚ Μ‚ VERB iajs-3911 78 102 οΏ½ οΏ½ NOUN iajs-3911 78 103 π›Όπœ† π›Όπœ† X iajs-3911 78 104 = = SYM iajs-3911 78 105 1 1 NUM iajs-3911 78 106 βˆ‘ βˆ‘ PROPN iajs-3911 78 107 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 78 108 ( ( PUNCT iajs-3911 78 109 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 78 110 ) ) PUNCT iajs-3911 78 111 2 2 NUM iajs-3911 78 112 𝑛 𝑛 PRON iajs-3911 78 113 𝑖=1 𝑖=1 PUNCT iajs-3911 78 114 to to PART iajs-3911 78 115 estimate estimate VERB iajs-3911 78 116 the the DET iajs-3911 78 117 parameter parameter NOUN iajs-3911 78 118 𝛼 𝛼 NOUN iajs-3911 78 119 at at ADP iajs-3911 78 120 case case NOUN iajs-3911 78 121 of of ADP iajs-3911 78 122 squared square VERB iajs-3911 78 123 error error NOUN iajs-3911 78 124 loss loss NOUN iajs-3911 78 125 function function NOUN iajs-3911 78 126 ( ( PUNCT iajs-3911 78 127 13 13 NUM iajs-3911 78 128 ) ) PUNCT iajs-3911 78 129 , , PUNCT iajs-3911 78 130 assuming assume VERB iajs-3911 78 131 that that SCONJ iajs-3911 78 132 πœ† πœ† NOUN iajs-3911 78 133 is be AUX iajs-3911 78 134 information information NOUN iajs-3911 78 135 . . PUNCT iajs-3911 79 1 οΏ½ οΏ½ PROPN iajs-3911 79 2 Μ‚ Μ‚ VERB iajs-3911 79 3 οΏ½ οΏ½ NOUN iajs-3911 79 4 𝐿𝐴𝐸 𝐿𝐴𝐸 NOUN iajs-3911 79 5 = = SYM iajs-3911 79 6 οΏ½ οΏ½ PROPN iajs-3911 79 7 Μ‚ Μ‚ NUM iajs-3911 79 8 οΏ½ οΏ½ NOUN iajs-3911 79 9 + + CCONJ iajs-3911 79 10 [ [ X iajs-3911 79 11 ( ( PUNCT iajs-3911 79 12 βˆ’πœƒ βˆ’πœƒ NOUN iajs-3911 79 13 ) ) PUNCT iajs-3911 79 14 ( ( PUNCT iajs-3911 79 15 1 1 NUM iajs-3911 79 16 βˆ‘ βˆ‘ NOUN iajs-3911 79 17 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 79 18 2 2 NUM iajs-3911 79 19 ( ( PUNCT iajs-3911 79 20 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 79 21 ) ) PUNCT iajs-3911 79 22 2 2 NUM iajs-3911 79 23 𝑛 𝑛 PRON iajs-3911 79 24 𝑖=1 𝑖=1 PROPN iajs-3911 79 25 ) ) PUNCT iajs-3911 80 1 + + CCONJ iajs-3911 80 2 ( ( PUNCT iajs-3911 80 3 βˆ’πœƒ βˆ’πœƒ NOUN iajs-3911 80 4 ) ) PUNCT iajs-3911 80 5 ( ( PUNCT iajs-3911 80 6 1 1 NUM iajs-3911 80 7 βˆ‘ βˆ‘ SYM iajs-3911 80 8 1 1 NUM iajs-3911 80 9 ( ( PUNCT iajs-3911 80 10 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 80 11 ) ) PUNCT iajs-3911 80 12 2 2 NUM iajs-3911 80 13 𝑛 𝑛 PROPN iajs-3911 80 14 𝑖=1 𝑖=1 PROPN iajs-3911 80 15 ) ) PUNCT iajs-3911 80 16 ] ] PUNCT iajs-3911 80 17 ihjpas ihjpas PROPN iajs-3911 80 18 . . PUNCT iajs-3911 81 1 2025,38(2 2025,38(2 NOUN iajs-3911 81 2 ) ) PUNCT iajs-3911 82 1 406 406 NUM iajs-3911 83 1 + + CCONJ iajs-3911 83 2 1 1 NUM iajs-3911 83 3 2 2 NUM iajs-3911 83 4 [ [ PUNCT iajs-3911 83 5 1 1 NUM iajs-3911 83 6 βˆ‘ βˆ‘ PROPN iajs-3911 83 7 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 83 8 ( ( PUNCT iajs-3911 83 9 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 83 10 ) ) PUNCT iajs-3911 83 11 2 2 NUM iajs-3911 83 12 𝑛 𝑛 PRON iajs-3911 83 13 𝑖=1 𝑖=1 PUNCT iajs-3911 83 14 ( ( PUNCT iajs-3911 83 15 2βˆ‘ 2βˆ‘ NUM iajs-3911 83 16 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 83 17 3 3 NUM iajs-3911 83 18 ( ( PUNCT iajs-3911 83 19 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 83 20 ) ) PUNCT iajs-3911 83 21 3 3 NUM iajs-3911 83 22 𝑛 𝑛 PROPN iajs-3911 83 23 𝑖=1 𝑖=1 PROPN iajs-3911 83 24 ( ( PUNCT iajs-3911 83 25 1 1 NUM iajs-3911 83 26 βˆ‘ βˆ‘ PROPN iajs-3911 83 27 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 83 28 2 2 NUM iajs-3911 83 29 ( ( PUNCT iajs-3911 83 30 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 83 31 ) ) PUNCT iajs-3911 83 32 2 2 NUM iajs-3911 83 33 𝑛 𝑛 PRON iajs-3911 83 34 𝑖=1 𝑖=1 PUNCT iajs-3911 83 35 ) ) PUNCT iajs-3911 84 1 + + CCONJ iajs-3911 84 2 2βˆ‘ 2βˆ‘ NUM iajs-3911 84 3 𝑑𝑖 𝑑𝑖 PRON iajs-3911 84 4 2 2 NUM iajs-3911 84 5 ( ( PUNCT iajs-3911 84 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 84 7 ) ) PUNCT iajs-3911 84 8 3 3 NUM iajs-3911 84 9 𝑛 𝑛 PROPN iajs-3911 84 10 𝑖=1 𝑖=1 PROPN iajs-3911 84 11 ( ( PUNCT iajs-3911 84 12 1 1 NUM iajs-3911 84 13 βˆ‘ βˆ‘ PROPN iajs-3911 84 14 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 84 15 ( ( PUNCT iajs-3911 84 16 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 84 17 ) ) PUNCT iajs-3911 84 18 2 2 NUM iajs-3911 84 19 𝑛 𝑛 PRON iajs-3911 84 20 𝑖=1 𝑖=1 PUNCT iajs-3911 84 21 ) ) PUNCT iajs-3911 85 1 +2βˆ‘ +2βˆ‘ ADV iajs-3911 85 2 𝑑𝑖 𝑑𝑖 DET iajs-3911 85 3 2 2 NUM iajs-3911 85 4 ( ( PUNCT iajs-3911 85 5 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 85 6 ) ) PUNCT iajs-3911 85 7 3 3 NUM iajs-3911 85 8 𝑛 𝑛 PROPN iajs-3911 85 9 𝑖=1 𝑖=1 PROPN iajs-3911 85 10 ( ( PUNCT iajs-3911 85 11 1 1 NUM iajs-3911 85 12 βˆ‘ βˆ‘ PROPN iajs-3911 85 13 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 85 14 ( ( PUNCT iajs-3911 85 15 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 85 16 ) ) PUNCT iajs-3911 85 17 2 2 NUM iajs-3911 85 18 𝑛 𝑛 PRON iajs-3911 85 19 𝑖=1 𝑖=1 PUNCT iajs-3911 85 20 ) ) PUNCT iajs-3911 86 1 + + CCONJ iajs-3911 86 2 2βˆ‘ 2βˆ‘ NUM iajs-3911 86 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 86 4 ( ( PUNCT iajs-3911 86 5 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 86 6 ) ) PUNCT iajs-3911 86 7 3 3 NUM iajs-3911 86 8 𝑛 𝑛 PROPN iajs-3911 86 9 𝑖=1 𝑖=1 PROPN iajs-3911 86 10 ( ( PUNCT iajs-3911 86 11 1 1 NUM iajs-3911 86 12 βˆ‘ βˆ‘ SYM iajs-3911 86 13 1 1 NUM iajs-3911 86 14 ( ( PUNCT iajs-3911 86 15 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 86 16 ) ) PUNCT iajs-3911 86 17 2 2 NUM iajs-3911 86 18 𝑛 𝑛 PRON iajs-3911 86 19 𝑖=1 𝑖=1 PROPN iajs-3911 86 20 ) ) PUNCT iajs-3911 86 21 ) ) PUNCT iajs-3911 87 1 + + CCONJ iajs-3911 87 2 1 1 NUM iajs-3911 87 3 βˆ‘ βˆ‘ SYM iajs-3911 87 4 1 1 NUM iajs-3911 87 5 ( ( PUNCT iajs-3911 87 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 87 7 ) ) PUNCT iajs-3911 87 8 2 2 NUM iajs-3911 87 9 𝑛 𝑛 PRON iajs-3911 87 10 𝑖=1 𝑖=1 PUNCT iajs-3911 87 11 ( ( PUNCT iajs-3911 87 12 2βˆ‘ 2βˆ‘ X iajs-3911 87 13 𝑑𝑖 𝑑𝑖 SYM iajs-3911 87 14 2 2 NUM iajs-3911 87 15 ( ( PUNCT iajs-3911 87 16 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 87 17 ) ) PUNCT iajs-3911 87 18 3 3 NUM iajs-3911 87 19 𝑛 𝑛 PROPN iajs-3911 87 20 𝑖=1 𝑖=1 PROPN iajs-3911 87 21 ( ( PUNCT iajs-3911 87 22 1 1 NUM iajs-3911 87 23 βˆ‘ βˆ‘ PROPN iajs-3911 87 24 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 87 25 2 2 NUM iajs-3911 87 26 ( ( PUNCT iajs-3911 87 27 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 87 28 ) ) PUNCT iajs-3911 87 29 2 2 NUM iajs-3911 87 30 𝑛 𝑛 PRON iajs-3911 87 31 𝑖=1 𝑖=1 PUNCT iajs-3911 87 32 ) ) PUNCT iajs-3911 88 1 + + CCONJ iajs-3911 89 1 2βˆ‘ 2βˆ‘ NUM iajs-3911 89 2 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 89 3 ( ( PUNCT iajs-3911 89 4 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 89 5 ) ) PUNCT iajs-3911 89 6 3 3 NUM iajs-3911 89 7 𝑛 𝑛 PROPN iajs-3911 89 8 𝑖=1 𝑖=1 PROPN iajs-3911 89 9 ( ( PUNCT iajs-3911 89 10 1 1 NUM iajs-3911 89 11 βˆ‘ βˆ‘ PROPN iajs-3911 89 12 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 89 13 ( ( PUNCT iajs-3911 89 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 89 15 ) ) PUNCT iajs-3911 89 16 2 2 NUM iajs-3911 89 17 𝑛 𝑛 PRON iajs-3911 89 18 𝑖=1 𝑖=1 PUNCT iajs-3911 89 19 ) ) PUNCT iajs-3911 90 1 +2βˆ‘ +2βˆ‘ ADP iajs-3911 90 2 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 90 3 ( ( PUNCT iajs-3911 90 4 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 90 5 ) ) PUNCT iajs-3911 90 6 3 3 NUM iajs-3911 90 7 𝑛 𝑛 PROPN iajs-3911 90 8 𝑖=1 𝑖=1 PROPN iajs-3911 90 9 ( ( PUNCT iajs-3911 90 10 1 1 NUM iajs-3911 90 11 βˆ‘ βˆ‘ PROPN iajs-3911 90 12 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 90 13 ( ( PUNCT iajs-3911 90 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 90 15 ) ) PUNCT iajs-3911 90 16 2 2 NUM iajs-3911 90 17 𝑛 𝑛 PRON iajs-3911 90 18 𝑖=1 𝑖=1 PUNCT iajs-3911 90 19 ) ) PUNCT iajs-3911 91 1 + + CCONJ iajs-3911 92 1 2βˆ‘ 2βˆ‘ NUM iajs-3911 92 2 1 1 NUM iajs-3911 92 3 ( ( PUNCT iajs-3911 92 4 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 92 5 ) ) PUNCT iajs-3911 92 6 3 3 NUM iajs-3911 92 7 𝑛 𝑛 PROPN iajs-3911 92 8 𝑖=1 𝑖=1 PROPN iajs-3911 92 9 ( ( PUNCT iajs-3911 92 10 1 1 NUM iajs-3911 92 11 βˆ‘ βˆ‘ SYM iajs-3911 92 12 1 1 NUM iajs-3911 92 13 ( ( PUNCT iajs-3911 92 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 92 15 ) ) PUNCT iajs-3911 92 16 2 2 NUM iajs-3911 92 17 𝑛 𝑛 PRON iajs-3911 92 18 𝑖=1 𝑖=1 PROPN iajs-3911 92 19 ) ) PUNCT iajs-3911 92 20 ) ) PUNCT iajs-3911 92 21 ] ] PUNCT iajs-3911 92 22 οΏ½ οΏ½ PROPN iajs-3911 92 23 Μ‚ Μ‚ VERB iajs-3911 92 24 οΏ½ οΏ½ NOUN iajs-3911 92 25 𝐿𝐴𝐸 𝐿𝐴𝐸 NOUN iajs-3911 92 26 = = SYM iajs-3911 92 27 οΏ½ οΏ½ PROPN iajs-3911 92 28 Μ‚ Μ‚ NUM iajs-3911 92 29 οΏ½ οΏ½ NOUN iajs-3911 92 30 + + PUNCT iajs-3911 93 1 [ [ X iajs-3911 93 2 βˆ’ βˆ’ X iajs-3911 93 3 πœƒ πœƒ X iajs-3911 93 4 βˆ‘ βˆ‘ PROPN iajs-3911 93 5 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 93 6 2 2 NUM iajs-3911 93 7 ( ( PUNCT iajs-3911 93 8 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 93 9 ) ) PUNCT iajs-3911 93 10 2 2 NUM iajs-3911 93 11 𝑛 𝑛 PRON iajs-3911 93 12 𝑖=1 𝑖=1 PUNCT iajs-3911 93 13 βˆ’ βˆ’ PROPN iajs-3911 93 14 πœƒ πœƒ NOUN iajs-3911 93 15 βˆ‘ βˆ‘ PROPN iajs-3911 93 16 1 1 NUM iajs-3911 93 17 ( ( PUNCT iajs-3911 93 18 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 93 19 ) ) PUNCT iajs-3911 93 20 2 2 NUM iajs-3911 93 21 𝑛 𝑛 PRON iajs-3911 93 22 𝑖=1 𝑖=1 PUNCT iajs-3911 93 23 ] ] PUNCT iajs-3911 94 1 + + CCONJ iajs-3911 94 2 1 1 NUM iajs-3911 94 3 βˆ‘ βˆ‘ PROPN iajs-3911 94 4 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 94 5 ( ( PUNCT iajs-3911 94 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 94 7 ) ) PUNCT iajs-3911 94 8 2 2 NUM iajs-3911 94 9 𝑛 𝑛 DET iajs-3911 94 10 𝑖=1 𝑖=1 PROPN iajs-3911 95 1 ( ( PUNCT iajs-3911 95 2 βˆ‘ βˆ‘ PROPN iajs-3911 95 3 𝑑𝑖 𝑑𝑖 X iajs-3911 95 4 3 3 NUM iajs-3911 95 5 ( ( PUNCT iajs-3911 95 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 95 7 ) ) PUNCT iajs-3911 95 8 3 3 NUM iajs-3911 95 9 𝑛 𝑛 NOUN iajs-3911 95 10 𝑖=1 𝑖=1 PUNCT iajs-3911 95 11 βˆ‘ βˆ‘ PROPN iajs-3911 95 12 𝑑𝑖 𝑑𝑖 SYM iajs-3911 95 13 2 2 NUM iajs-3911 95 14 ( ( PUNCT iajs-3911 95 15 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 95 16 ) ) PUNCT iajs-3911 95 17 2 2 NUM iajs-3911 95 18 𝑛 𝑛 PRON iajs-3911 95 19 𝑖=1 𝑖=1 PROPN iajs-3911 96 1 + + CCONJ iajs-3911 96 2 βˆ‘ βˆ‘ PROPN iajs-3911 96 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 96 4 2 2 NUM iajs-3911 96 5 ( ( PUNCT iajs-3911 96 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 96 7 ) ) PUNCT iajs-3911 96 8 3 3 NUM iajs-3911 96 9 𝑛 𝑛 NOUN iajs-3911 96 10 𝑖=1 𝑖=1 PUNCT iajs-3911 96 11 βˆ‘ βˆ‘ ADV iajs-3911 96 12 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 96 13 ( ( PUNCT iajs-3911 96 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 96 15 ) ) PUNCT iajs-3911 96 16 2 2 NUM iajs-3911 96 17 𝑛 𝑛 PRON iajs-3911 96 18 𝑖=1 𝑖=1 PROPN iajs-3911 97 1 + + CCONJ iajs-3911 97 2 βˆ‘ βˆ‘ PROPN iajs-3911 97 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 97 4 2 2 NUM iajs-3911 97 5 ( ( PUNCT iajs-3911 97 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 97 7 ) ) PUNCT iajs-3911 97 8 3 3 NUM iajs-3911 97 9 𝑛 𝑛 NOUN iajs-3911 97 10 𝑖=1 𝑖=1 PUNCT iajs-3911 97 11 βˆ‘ βˆ‘ PROPN iajs-3911 97 12 𝑑𝑖 𝑑𝑖 SYM iajs-3911 97 13 2 2 NUM iajs-3911 97 14 ( ( PUNCT iajs-3911 97 15 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 97 16 ) ) PUNCT iajs-3911 97 17 2 2 NUM iajs-3911 97 18 𝑛 𝑛 PRON iajs-3911 97 19 𝑖=1 𝑖=1 PROPN iajs-3911 97 20 + + CCONJ iajs-3911 97 21 βˆ‘ βˆ‘ PROPN iajs-3911 97 22 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 97 23 ( ( PUNCT iajs-3911 97 24 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 97 25 ) ) PUNCT iajs-3911 97 26 3 3 NUM iajs-3911 97 27 𝑛 𝑛 PRON iajs-3911 97 28 𝑖=1 𝑖=1 PUNCT iajs-3911 97 29 βˆ‘ βˆ‘ PROPN iajs-3911 97 30 1 1 NUM iajs-3911 97 31 ( ( PUNCT iajs-3911 97 32 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 97 33 ) ) PUNCT iajs-3911 97 34 2 2 NUM iajs-3911 97 35 𝑛 𝑛 PRON iajs-3911 97 36 𝑖=1 𝑖=1 PROPN iajs-3911 97 37 ) ) PUNCT iajs-3911 98 1 + + CCONJ iajs-3911 98 2 1 1 NUM iajs-3911 98 3 βˆ‘ βˆ‘ SYM iajs-3911 98 4 1 1 NUM iajs-3911 98 5 ( ( PUNCT iajs-3911 98 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 98 7 ) ) PUNCT iajs-3911 98 8 2 2 NUM iajs-3911 98 9 𝑛 𝑛 PRON iajs-3911 98 10 𝑖=1 𝑖=1 PROPN iajs-3911 99 1 ( ( PUNCT iajs-3911 99 2 βˆ‘ βˆ‘ PROPN iajs-3911 99 3 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 99 4 2 2 NUM iajs-3911 99 5 ( ( PUNCT iajs-3911 99 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 99 7 ) ) PUNCT iajs-3911 99 8 3 3 NUM iajs-3911 99 9 𝑛 𝑛 NOUN iajs-3911 99 10 𝑖=1 𝑖=1 PUNCT iajs-3911 99 11 βˆ‘ βˆ‘ PROPN iajs-3911 99 12 𝑑𝑖 𝑑𝑖 SYM iajs-3911 99 13 2 2 NUM iajs-3911 99 14 ( ( PUNCT iajs-3911 99 15 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 99 16 ) ) PUNCT iajs-3911 99 17 2 2 NUM iajs-3911 99 18 𝑛 𝑛 PRON iajs-3911 99 19 𝑖=1 𝑖=1 PROPN iajs-3911 100 1 + + CCONJ iajs-3911 100 2 βˆ‘ βˆ‘ PROPN iajs-3911 100 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 100 4 ( ( PUNCT iajs-3911 100 5 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 100 6 ) ) PUNCT iajs-3911 100 7 3 3 NUM iajs-3911 100 8 𝑛 𝑛 NOUN iajs-3911 100 9 𝑖=1 𝑖=1 PUNCT iajs-3911 100 10 βˆ‘ βˆ‘ ADV iajs-3911 100 11 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 100 12 ( ( PUNCT iajs-3911 100 13 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 100 14 ) ) PUNCT iajs-3911 100 15 2 2 NUM iajs-3911 100 16 𝑛 𝑛 PRON iajs-3911 100 17 𝑖=1 𝑖=1 PROPN iajs-3911 100 18 + + CCONJ iajs-3911 100 19 βˆ‘ βˆ‘ PROPN iajs-3911 100 20 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 100 21 ( ( PUNCT iajs-3911 100 22 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 100 23 ) ) PUNCT iajs-3911 100 24 3 3 NUM iajs-3911 100 25 𝑛 𝑛 NOUN iajs-3911 100 26 𝑖=1 𝑖=1 PUNCT iajs-3911 100 27 βˆ‘ βˆ‘ ADV iajs-3911 100 28 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 100 29 ( ( PUNCT iajs-3911 100 30 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 100 31 ) ) PUNCT iajs-3911 100 32 2 2 NUM iajs-3911 100 33 𝑛 𝑛 PRON iajs-3911 100 34 𝑖=1 𝑖=1 PROPN iajs-3911 101 1 + + CCONJ iajs-3911 101 2 βˆ‘ βˆ‘ SYM iajs-3911 101 3 1 1 NUM iajs-3911 101 4 ( ( PUNCT iajs-3911 101 5 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 101 6 ) ) PUNCT iajs-3911 101 7 3 3 NUM iajs-3911 101 8 𝑛 𝑛 PRON iajs-3911 101 9 𝑖=1 𝑖=1 PUNCT iajs-3911 101 10 βˆ‘ βˆ‘ PROPN iajs-3911 101 11 1 1 NUM iajs-3911 101 12 ( ( PUNCT iajs-3911 101 13 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 101 14 ) ) PUNCT iajs-3911 101 15 2 2 NUM iajs-3911 101 16 𝑛 𝑛 PRON iajs-3911 101 17 𝑖=1 𝑖=1 PROPN iajs-3911 101 18 ) ) PUNCT iajs-3911 101 19 ( ( PUNCT iajs-3911 101 20 20 20 NUM iajs-3911 101 21 ) ) PUNCT iajs-3911 101 22 to to PART iajs-3911 101 23 estimate estimate VERB iajs-3911 101 24 the the DET iajs-3911 101 25 parameter parameter NOUN iajs-3911 101 26 πœ† πœ† ADP iajs-3911 101 27 at at ADP iajs-3911 101 28 case case NOUN iajs-3911 101 29 of of ADP iajs-3911 101 30 squared square VERB iajs-3911 101 31 error error NOUN iajs-3911 101 32 loss loss NOUN iajs-3911 101 33 function function NOUN iajs-3911 101 34 ( ( PUNCT iajs-3911 101 35 14 14 NUM iajs-3911 101 36 ) ) PUNCT iajs-3911 101 37 , , PUNCT iajs-3911 101 38 assuming assume VERB iajs-3911 101 39 that that SCONJ iajs-3911 101 40 𝛼 𝛼 PROPN iajs-3911 101 41 is be AUX iajs-3911 101 42 information information NOUN iajs-3911 101 43 . . PUNCT iajs-3911 102 1 we we PRON iajs-3911 102 2 choose choose VERB iajs-3911 102 3 : : PUNCT iajs-3911 102 4 ( ( PUNCT iajs-3911 102 5 οΏ½ οΏ½ NOUN iajs-3911 102 6 Μ‚ Μ‚ SYM iajs-3911 102 7 οΏ½ οΏ½ PROPN iajs-3911 102 8 , , PUNCT iajs-3911 102 9 οΏ½ οΏ½ PROPN iajs-3911 102 10 Μ‚ Μ‚ NOUN iajs-3911 102 11 οΏ½ οΏ½ NOUN iajs-3911 102 12 ) ) PUNCT iajs-3911 102 13 = = SYM iajs-3911 103 1 πœ† πœ† PROPN iajs-3911 103 2 , , PUNCT iajs-3911 103 3 οΏ½ οΏ½ PROPN iajs-3911 103 4 Μ‚ Μ‚ NOUN iajs-3911 103 5 οΏ½ οΏ½ PROPN iajs-3911 103 6 πœ† πœ† PRON iajs-3911 103 7 = = SYM iajs-3911 103 8 πœ•π‘’( πœ•π‘’( PROPN iajs-3911 103 9 οΏ½ οΏ½ PROPN iajs-3911 103 10 Μ‚ Μ‚ VERB iajs-3911 103 11 οΏ½ οΏ½ PROPN iajs-3911 103 12 , , PUNCT iajs-3911 103 13 οΏ½ οΏ½ PROPN iajs-3911 103 14 Μ‚ Μ‚ NOUN iajs-3911 103 15 οΏ½ οΏ½ NOUN iajs-3911 103 16 ) ) PUNCT iajs-3911 103 17 πœ•πœ† πœ•πœ† NOUN iajs-3911 103 18 = = SYM iajs-3911 103 19 1 1 NUM iajs-3911 103 20 , , PUNCT iajs-3911 103 21 οΏ½ οΏ½ NOUN iajs-3911 103 22 Μ‚ Μ‚ NOUN iajs-3911 103 23 οΏ½ οΏ½ NOUN iajs-3911 103 24 𝛼 𝛼 NOUN iajs-3911 103 25 = = SYM iajs-3911 103 26 0 0 NUM iajs-3911 103 27 , , PUNCT iajs-3911 103 28 οΏ½ οΏ½ PROPN iajs-3911 103 29 Μ‚ Μ‚ NOUN iajs-3911 103 30 οΏ½ οΏ½ NOUN iajs-3911 103 31 𝛼𝛼 𝛼𝛼 ADP iajs-3911 103 32 = = SYM iajs-3911 103 33 0 0 NUM iajs-3911 103 34 , , PUNCT iajs-3911 103 35 οΏ½ οΏ½ NOUN iajs-3911 103 36 Μ‚ Μ‚ NOUN iajs-3911 103 37 οΏ½ οΏ½ NOUN iajs-3911 103 38 πœ†πœ† πœ†πœ† NOUN iajs-3911 103 39 = = SYM iajs-3911 103 40 0 0 NUM iajs-3911 103 41 , , PUNCT iajs-3911 103 42 οΏ½ οΏ½ NOUN iajs-3911 103 43 Μ‚ Μ‚ NOUN iajs-3911 103 44 οΏ½ οΏ½ NOUN iajs-3911 103 45 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 103 46 = = SYM iajs-3911 103 47 0 0 NUM iajs-3911 103 48 , , PUNCT iajs-3911 103 49 οΏ½ οΏ½ NOUN iajs-3911 103 50 Μ‚ Μ‚ VERB iajs-3911 103 51 οΏ½ οΏ½ NOUN iajs-3911 103 52 π›Όπœ† π›Όπœ† X iajs-3911 103 53 = = SYM iajs-3911 103 54 0 0 NUM iajs-3911 103 55 ΞΉ(π‘₯ ΞΉ(π‘₯ NOUN iajs-3911 103 56 ) ) PUNCT iajs-3911 103 57 = = SYM iajs-3911 103 58 οΏ½ οΏ½ PROPN iajs-3911 103 59 Μ‚ Μ‚ NUM iajs-3911 103 60 οΏ½ οΏ½ NOUN iajs-3911 103 61 + + CCONJ iajs-3911 103 62 1 1 NUM iajs-3911 103 63 2 2 NUM iajs-3911 103 64 [ [ X iajs-3911 103 65 ( ( PUNCT iajs-3911 103 66 2 2 NUM iajs-3911 103 67 οΏ½ οΏ½ NOUN iajs-3911 103 68 Μ‚ Μ‚ NUM iajs-3911 103 69 οΏ½ οΏ½ PROPN iajs-3911 103 70 πœ† πœ† NOUN iajs-3911 103 71 οΏ½ οΏ½ PROPN iajs-3911 103 72 Μ‚ Μ‚ SYM iajs-3911 103 73 οΏ½ οΏ½ NOUN iajs-3911 103 74 πœ†) πœ†) SYM iajs-3911 103 75 οΏ½ οΏ½ PROPN iajs-3911 103 76 Μ‚ Μ‚ NOUN iajs-3911 103 77 οΏ½ οΏ½ NOUN iajs-3911 103 78 πœ†πœ† πœ†πœ† VERB iajs-3911 103 79 + + CCONJ iajs-3911 103 80 ( ( PUNCT iajs-3911 103 81 2 2 NUM iajs-3911 103 82 οΏ½ οΏ½ NOUN iajs-3911 103 83 Μ‚ Μ‚ NUM iajs-3911 103 84 οΏ½ οΏ½ PROPN iajs-3911 103 85 πœ† πœ† NOUN iajs-3911 103 86 οΏ½ οΏ½ PROPN iajs-3911 103 87 Μ‚ Μ‚ VERB iajs-3911 103 88 οΏ½ οΏ½ PROPN iajs-3911 103 89 𝛼) 𝛼) PROPN iajs-3911 103 90 οΏ½ οΏ½ PROPN iajs-3911 103 91 Μ‚ Μ‚ SYM iajs-3911 103 92 οΏ½ οΏ½ NOUN iajs-3911 103 93 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 103 94 ] ] X iajs-3911 104 1 + + CCONJ iajs-3911 104 2 1 1 NUM iajs-3911 104 3 2 2 NUM iajs-3911 104 4 [ [ X iajs-3911 104 5 ( ( PUNCT iajs-3911 104 6 οΏ½ οΏ½ NOUN iajs-3911 104 7 Μ‚ Μ‚ NOUN iajs-3911 104 8 οΏ½ οΏ½ PROPN iajs-3911 104 9 πœ†πœ†)( πœ†πœ†)( SYM iajs-3911 104 10 οΏ½ οΏ½ PROPN iajs-3911 104 11 Μ‚ Μ‚ NOUN iajs-3911 104 12 οΏ½ οΏ½ NOUN iajs-3911 104 13 πœ†πœ†πœ† πœ†πœ†πœ† NOUN iajs-3911 104 14 οΏ½ οΏ½ PROPN iajs-3911 104 15 Μ‚ Μ‚ NOUN iajs-3911 104 16 οΏ½ οΏ½ NOUN iajs-3911 104 17 πœ†πœ† πœ†πœ† ADP iajs-3911 104 18 + + NUM iajs-3911 104 19 οΏ½ οΏ½ PROPN iajs-3911 104 20 Μ‚ Μ‚ SYM iajs-3911 104 21 οΏ½ οΏ½ PROPN iajs-3911 104 22 πœ†π›Όπœ† πœ†π›Όπœ† PROPN iajs-3911 104 23 οΏ½ οΏ½ PROPN iajs-3911 104 24 Μ‚ Μ‚ NOUN iajs-3911 104 25 οΏ½ οΏ½ NOUN iajs-3911 104 26 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 104 27 + + SYM iajs-3911 104 28 οΏ½ οΏ½ PROPN iajs-3911 104 29 Μ‚ Μ‚ NOUN iajs-3911 104 30 οΏ½ οΏ½ PROPN iajs-3911 104 31 π›Όπœ†πœ† π›Όπœ†πœ† ADJ iajs-3911 104 32 οΏ½ οΏ½ PROPN iajs-3911 104 33 Μ‚ Μ‚ VERB iajs-3911 104 34 οΏ½ οΏ½ NOUN iajs-3911 104 35 π›Όπœ† π›Όπœ† SYM iajs-3911 104 36 + + NUM iajs-3911 104 37 οΏ½ οΏ½ PROPN iajs-3911 104 38 Μ‚ Μ‚ SYM iajs-3911 104 39 οΏ½ οΏ½ PROPN iajs-3911 104 40 π›Όπ›Όπœ† π›Όπ›Όπœ† VERB iajs-3911 104 41 οΏ½ οΏ½ PROPN iajs-3911 104 42 Μ‚ Μ‚ NUM iajs-3911 104 43 οΏ½ οΏ½ NOUN iajs-3911 104 44 𝛼𝛼 𝛼𝛼 NOUN iajs-3911 104 45 ) ) PUNCT iajs-3911 104 46 + + PROPN iajs-3911 104 47 ( ( PUNCT iajs-3911 104 48 οΏ½ οΏ½ NOUN iajs-3911 104 49 Μ‚ Μ‚ SYM iajs-3911 104 50 οΏ½ οΏ½ PROPN iajs-3911 104 51 π›Όπœ†)( π›Όπœ†)( NOUN iajs-3911 104 52 οΏ½ οΏ½ PROPN iajs-3911 104 53 Μ‚ Μ‚ SYM iajs-3911 104 54 οΏ½ οΏ½ PROPN iajs-3911 104 55 π›Όπœ†πœ† π›Όπœ†πœ† ADJ iajs-3911 104 56 οΏ½ οΏ½ PROPN iajs-3911 104 57 Μ‚ Μ‚ NOUN iajs-3911 104 58 οΏ½ οΏ½ NOUN iajs-3911 104 59 πœ†πœ† πœ†πœ† ADP iajs-3911 104 60 + + NUM iajs-3911 104 61 οΏ½ οΏ½ PROPN iajs-3911 104 62 Μ‚ Μ‚ NOUN iajs-3911 104 63 οΏ½ οΏ½ PROPN iajs-3911 104 64 πœ†π›Όπ›Ό πœ†π›Όπ›Ό NOUN iajs-3911 104 65 οΏ½ οΏ½ PROPN iajs-3911 104 66 Μ‚ Μ‚ VERB iajs-3911 104 67 οΏ½ οΏ½ NOUN iajs-3911 104 68 πœ†π›Ό πœ†π›Ό NOUN iajs-3911 104 69 + + SYM iajs-3911 104 70 οΏ½ οΏ½ PROPN iajs-3911 104 71 Μ‚ Μ‚ NOUN iajs-3911 104 72 οΏ½ οΏ½ PROPN iajs-3911 104 73 π›Όπœ†π›Ό π›Όπœ†π›Ό NOUN iajs-3911 104 74 οΏ½ οΏ½ PROPN iajs-3911 104 75 Μ‚ Μ‚ VERB iajs-3911 104 76 οΏ½ οΏ½ NOUN iajs-3911 104 77 π›Όπœ† π›Όπœ† SYM iajs-3911 104 78 + + NUM iajs-3911 104 79 οΏ½ οΏ½ PROPN iajs-3911 104 80 Μ‚ Μ‚ NUM iajs-3911 104 81 οΏ½ οΏ½ NOUN iajs-3911 104 82 𝛼𝛼𝛼 𝛼𝛼𝛼 VERB iajs-3911 104 83 οΏ½ οΏ½ PROPN iajs-3911 104 84 Μ‚ Μ‚ PROPN iajs-3911 104 85 οΏ½ οΏ½ NOUN iajs-3911 104 86 𝛼𝛼 𝛼𝛼 NOUN iajs-3911 104 87 ) ) PUNCT iajs-3911 104 88 ] ] PUNCT iajs-3911 104 89 ( ( PUNCT iajs-3911 104 90 21 21 NUM iajs-3911 104 91 ) ) PUNCT iajs-3911 104 92 οΏ½ οΏ½ NOUN iajs-3911 104 93 Μ‚ Μ‚ VERB iajs-3911 104 94 οΏ½ οΏ½ NOUN iajs-3911 104 95 𝐿𝐴𝐸 𝐿𝐴𝐸 NOUN iajs-3911 104 96 = = SYM iajs-3911 104 97 οΏ½ οΏ½ PROPN iajs-3911 104 98 Μ‚ Μ‚ NUM iajs-3911 104 99 οΏ½ οΏ½ NOUN iajs-3911 104 100 + + CCONJ iajs-3911 105 1 [ [ X iajs-3911 105 2 ( ( PUNCT iajs-3911 105 3 βˆ’πœƒ βˆ’πœƒ NOUN iajs-3911 105 4 ) ) PUNCT iajs-3911 105 5 ( ( PUNCT iajs-3911 105 6 1 1 NUM iajs-3911 105 7 βˆ‘ βˆ‘ NOUN iajs-3911 105 8 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 105 9 2 2 NUM iajs-3911 105 10 ( ( PUNCT iajs-3911 105 11 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 105 12 ) ) PUNCT iajs-3911 105 13 2 2 NUM iajs-3911 105 14 𝑛 𝑛 PRON iajs-3911 105 15 𝑖=1 𝑖=1 PROPN iajs-3911 105 16 ) ) PUNCT iajs-3911 105 17 + + CCONJ iajs-3911 105 18 ( ( PUNCT iajs-3911 105 19 βˆ’πœƒ βˆ’πœƒ NOUN iajs-3911 105 20 ) ) PUNCT iajs-3911 105 21 ( ( PUNCT iajs-3911 105 22 1 1 NUM iajs-3911 105 23 βˆ‘ βˆ‘ PROPN iajs-3911 105 24 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 105 25 ( ( PUNCT iajs-3911 105 26 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 105 27 ) ) PUNCT iajs-3911 105 28 2 2 NUM iajs-3911 105 29 𝑛 𝑛 PROPN iajs-3911 105 30 𝑖=1 𝑖=1 PROPN iajs-3911 105 31 ) ) PUNCT iajs-3911 105 32 ] ] PUNCT iajs-3911 106 1 + + CCONJ iajs-3911 106 2 1 1 NUM iajs-3911 106 3 2 2 NUM iajs-3911 106 4 [ [ PUNCT iajs-3911 106 5 1 1 NUM iajs-3911 106 6 βˆ‘ βˆ‘ PROPN iajs-3911 106 7 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 106 8 ( ( PUNCT iajs-3911 106 9 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 106 10 ) ) PUNCT iajs-3911 106 11 2 2 NUM iajs-3911 106 12 𝑛 𝑛 PRON iajs-3911 106 13 𝑖=1 𝑖=1 PUNCT iajs-3911 106 14 ( ( PUNCT iajs-3911 106 15 2βˆ‘ 2βˆ‘ NUM iajs-3911 106 16 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 106 17 3 3 NUM iajs-3911 106 18 ( ( PUNCT iajs-3911 106 19 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 106 20 ) ) PUNCT iajs-3911 106 21 3 3 NUM iajs-3911 106 22 𝑛 𝑛 PROPN iajs-3911 106 23 𝑖=1 𝑖=1 PROPN iajs-3911 106 24 ( ( PUNCT iajs-3911 106 25 1 1 NUM iajs-3911 106 26 βˆ‘ βˆ‘ PROPN iajs-3911 106 27 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 106 28 2 2 NUM iajs-3911 106 29 ( ( PUNCT iajs-3911 106 30 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 106 31 ) ) PUNCT iajs-3911 106 32 2 2 NUM iajs-3911 106 33 𝑛 𝑛 PRON iajs-3911 106 34 𝑖=1 𝑖=1 PUNCT iajs-3911 106 35 ) ) PUNCT iajs-3911 107 1 + + CCONJ iajs-3911 107 2 2βˆ‘ 2βˆ‘ NUM iajs-3911 107 3 𝑑𝑖 𝑑𝑖 PRON iajs-3911 107 4 2 2 NUM iajs-3911 107 5 ( ( PUNCT iajs-3911 107 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 107 7 ) ) PUNCT iajs-3911 107 8 3 3 NUM iajs-3911 107 9 𝑛 𝑛 PROPN iajs-3911 107 10 𝑖=1 𝑖=1 PROPN iajs-3911 107 11 ( ( PUNCT iajs-3911 107 12 1 1 NUM iajs-3911 107 13 βˆ‘ βˆ‘ PROPN iajs-3911 107 14 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 107 15 ( ( PUNCT iajs-3911 107 16 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 107 17 ) ) PUNCT iajs-3911 107 18 2 2 NUM iajs-3911 107 19 𝑛 𝑛 PRON iajs-3911 107 20 𝑖=1 𝑖=1 PUNCT iajs-3911 107 21 ) ) PUNCT iajs-3911 108 1 +2βˆ‘ +2βˆ‘ ADV iajs-3911 108 2 𝑑𝑖 𝑑𝑖 DET iajs-3911 108 3 2 2 NUM iajs-3911 108 4 ( ( PUNCT iajs-3911 108 5 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 108 6 ) ) PUNCT iajs-3911 108 7 3 3 NUM iajs-3911 108 8 𝑛 𝑛 PROPN iajs-3911 108 9 𝑖=1 𝑖=1 PROPN iajs-3911 108 10 ( ( PUNCT iajs-3911 108 11 1 1 NUM iajs-3911 108 12 βˆ‘ βˆ‘ PROPN iajs-3911 108 13 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 108 14 ( ( PUNCT iajs-3911 108 15 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 108 16 ) ) PUNCT iajs-3911 108 17 2 2 NUM iajs-3911 108 18 𝑛 𝑛 PRON iajs-3911 108 19 𝑖=1 𝑖=1 PUNCT iajs-3911 108 20 ) ) PUNCT iajs-3911 109 1 + + CCONJ iajs-3911 109 2 2βˆ‘ 2βˆ‘ NUM iajs-3911 109 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 109 4 ( ( PUNCT iajs-3911 109 5 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 109 6 ) ) PUNCT iajs-3911 109 7 3 3 NUM iajs-3911 109 8 𝑛 𝑛 PROPN iajs-3911 109 9 𝑖=1 𝑖=1 PROPN iajs-3911 109 10 ( ( PUNCT iajs-3911 109 11 1 1 NUM iajs-3911 109 12 βˆ‘ βˆ‘ SYM iajs-3911 109 13 1 1 NUM iajs-3911 109 14 ( ( PUNCT iajs-3911 109 15 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 109 16 ) ) PUNCT iajs-3911 109 17 2 2 NUM iajs-3911 109 18 𝑛 𝑛 PRON iajs-3911 109 19 𝑖=1 𝑖=1 PROPN iajs-3911 109 20 ) ) PUNCT iajs-3911 109 21 ) ) PUNCT iajs-3911 110 1 + + CCONJ iajs-3911 110 2 1 1 NUM iajs-3911 110 3 βˆ‘ βˆ‘ NOUN iajs-3911 110 4 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 110 5 ( ( PUNCT iajs-3911 110 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 110 7 ) ) PUNCT iajs-3911 110 8 2 2 NUM iajs-3911 110 9 𝑛 𝑛 PRON iajs-3911 110 10 𝑖=1 𝑖=1 PUNCT iajs-3911 111 1 ( ( PUNCT iajs-3911 111 2 2βˆ‘ 2βˆ‘ X iajs-3911 111 3 𝑑𝑖 𝑑𝑖 SYM iajs-3911 111 4 2 2 NUM iajs-3911 111 5 ( ( PUNCT iajs-3911 111 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 111 7 ) ) PUNCT iajs-3911 111 8 3 3 NUM iajs-3911 111 9 𝑛 𝑛 PROPN iajs-3911 111 10 𝑖=1 𝑖=1 PROPN iajs-3911 111 11 ( ( PUNCT iajs-3911 111 12 1 1 NUM iajs-3911 111 13 βˆ‘ βˆ‘ PROPN iajs-3911 111 14 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 111 15 2 2 NUM iajs-3911 111 16 ( ( PUNCT iajs-3911 111 17 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 111 18 ) ) PUNCT iajs-3911 111 19 2 2 NUM iajs-3911 111 20 𝑛 𝑛 PRON iajs-3911 111 21 𝑖=1 𝑖=1 PUNCT iajs-3911 111 22 ) ) PUNCT iajs-3911 112 1 + + CCONJ iajs-3911 112 2 2βˆ‘ 2βˆ‘ NUM iajs-3911 112 3 𝑑𝑖 𝑑𝑖 PRON iajs-3911 112 4 2 2 NUM iajs-3911 112 5 ( ( PUNCT iajs-3911 112 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 112 7 ) ) PUNCT iajs-3911 112 8 3 3 NUM iajs-3911 112 9 𝑛 𝑛 PROPN iajs-3911 112 10 𝑖=1 𝑖=1 PROPN iajs-3911 112 11 ( ( PUNCT iajs-3911 112 12 1 1 NUM iajs-3911 112 13 βˆ‘ βˆ‘ PROPN iajs-3911 112 14 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 112 15 ( ( PUNCT iajs-3911 112 16 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 112 17 ) ) PUNCT iajs-3911 112 18 2 2 NUM iajs-3911 112 19 𝑛 𝑛 PRON iajs-3911 112 20 𝑖=1 𝑖=1 PUNCT iajs-3911 112 21 ) ) PUNCT iajs-3911 113 1 +2βˆ‘ +2βˆ‘ ADP iajs-3911 113 2 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 113 3 ( ( PUNCT iajs-3911 113 4 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 113 5 ) ) PUNCT iajs-3911 113 6 3 3 NUM iajs-3911 113 7 𝑛 𝑛 PROPN iajs-3911 113 8 𝑖=1 𝑖=1 PROPN iajs-3911 113 9 ( ( PUNCT iajs-3911 113 10 1 1 NUM iajs-3911 113 11 βˆ‘ βˆ‘ PROPN iajs-3911 113 12 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 113 13 ( ( PUNCT iajs-3911 113 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 113 15 ) ) PUNCT iajs-3911 113 16 2 2 NUM iajs-3911 113 17 𝑛 𝑛 PRON iajs-3911 113 18 𝑖=1 𝑖=1 PUNCT iajs-3911 113 19 ) ) PUNCT iajs-3911 114 1 + + CCONJ iajs-3911 115 1 2βˆ‘ 2βˆ‘ NUM iajs-3911 115 2 1 1 NUM iajs-3911 115 3 ( ( PUNCT iajs-3911 115 4 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 115 5 ) ) PUNCT iajs-3911 115 6 3 3 NUM iajs-3911 115 7 𝑛 𝑛 PROPN iajs-3911 115 8 𝑖=1 𝑖=1 PROPN iajs-3911 115 9 ( ( PUNCT iajs-3911 115 10 1 1 NUM iajs-3911 115 11 βˆ‘ βˆ‘ SYM iajs-3911 115 12 1 1 NUM iajs-3911 115 13 ( ( PUNCT iajs-3911 115 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 115 15 ) ) PUNCT iajs-3911 115 16 2 2 NUM iajs-3911 115 17 𝑛 𝑛 PRON iajs-3911 115 18 𝑖=1 𝑖=1 PROPN iajs-3911 115 19 ) ) PUNCT iajs-3911 115 20 ) ) PUNCT iajs-3911 115 21 ] ] PUNCT iajs-3911 115 22 οΏ½ οΏ½ PROPN iajs-3911 115 23 Μ‚ Μ‚ VERB iajs-3911 115 24 οΏ½ οΏ½ NOUN iajs-3911 115 25 𝐿𝐴𝐸 𝐿𝐴𝐸 NOUN iajs-3911 115 26 = = SYM iajs-3911 115 27 οΏ½ οΏ½ PROPN iajs-3911 115 28 Μ‚ Μ‚ NUM iajs-3911 115 29 οΏ½ οΏ½ NOUN iajs-3911 115 30 + + PUNCT iajs-3911 116 1 [ [ X iajs-3911 116 2 βˆ’ βˆ’ X iajs-3911 116 3 πœƒ πœƒ X iajs-3911 116 4 βˆ‘ βˆ‘ PROPN iajs-3911 116 5 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 116 6 2 2 NUM iajs-3911 116 7 ( ( PUNCT iajs-3911 116 8 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 116 9 ) ) PUNCT iajs-3911 116 10 2 2 NUM iajs-3911 116 11 𝑛 𝑛 PRON iajs-3911 116 12 𝑖=1 𝑖=1 PROPN iajs-3911 116 13 βˆ’ βˆ’ X iajs-3911 116 14 πœƒ πœƒ X iajs-3911 116 15 βˆ‘ βˆ‘ PROPN iajs-3911 116 16 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 116 17 ( ( PUNCT iajs-3911 116 18 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 116 19 ) ) PUNCT iajs-3911 116 20 2 2 NUM iajs-3911 116 21 𝑛 𝑛 PRON iajs-3911 116 22 𝑖=1 𝑖=1 PROPN iajs-3911 116 23 ] ] PUNCT iajs-3911 116 24 ihjpas ihjpas PROPN iajs-3911 116 25 . . PUNCT iajs-3911 117 1 2025,38(2 2025,38(2 NOUN iajs-3911 117 2 ) ) PUNCT iajs-3911 117 3 407 407 NUM iajs-3911 118 1 + + CCONJ iajs-3911 118 2 1 1 NUM iajs-3911 118 3 βˆ‘ βˆ‘ NOUN iajs-3911 118 4 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 118 5 ( ( PUNCT iajs-3911 118 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 118 7 ) ) PUNCT iajs-3911 118 8 2 2 NUM iajs-3911 118 9 𝑛 𝑛 PRON iajs-3911 118 10 𝑖=1 𝑖=1 PROPN iajs-3911 118 11 ( ( PUNCT iajs-3911 118 12 βˆ‘ βˆ‘ PROPN iajs-3911 118 13 𝑑𝑖 𝑑𝑖 X iajs-3911 118 14 3 3 NUM iajs-3911 118 15 ( ( PUNCT iajs-3911 118 16 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 118 17 ) ) PUNCT iajs-3911 118 18 3 3 NUM iajs-3911 118 19 𝑛 𝑛 NOUN iajs-3911 118 20 𝑖=1 𝑖=1 PUNCT iajs-3911 118 21 βˆ‘ βˆ‘ PROPN iajs-3911 118 22 𝑑𝑖 𝑑𝑖 SYM iajs-3911 118 23 2 2 NUM iajs-3911 118 24 ( ( PUNCT iajs-3911 118 25 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 118 26 ) ) PUNCT iajs-3911 118 27 2 2 NUM iajs-3911 118 28 𝑛 𝑛 PRON iajs-3911 118 29 𝑖=1 𝑖=1 PROPN iajs-3911 119 1 + + CCONJ iajs-3911 119 2 βˆ‘ βˆ‘ PROPN iajs-3911 119 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 119 4 2 2 NUM iajs-3911 119 5 ( ( PUNCT iajs-3911 119 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 119 7 ) ) PUNCT iajs-3911 119 8 3 3 NUM iajs-3911 119 9 𝑛 𝑛 NOUN iajs-3911 119 10 𝑖=1 𝑖=1 PUNCT iajs-3911 119 11 βˆ‘ βˆ‘ ADV iajs-3911 119 12 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 119 13 ( ( PUNCT iajs-3911 119 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 119 15 ) ) PUNCT iajs-3911 119 16 2 2 NUM iajs-3911 119 17 𝑛 𝑛 PRON iajs-3911 119 18 𝑖=1 𝑖=1 PROPN iajs-3911 120 1 + + CCONJ iajs-3911 120 2 βˆ‘ βˆ‘ PROPN iajs-3911 120 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 120 4 2 2 NUM iajs-3911 120 5 ( ( PUNCT iajs-3911 120 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 120 7 ) ) PUNCT iajs-3911 120 8 3 3 NUM iajs-3911 120 9 𝑛 𝑛 NOUN iajs-3911 120 10 𝑖=1 𝑖=1 PUNCT iajs-3911 120 11 βˆ‘ βˆ‘ ADV iajs-3911 120 12 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 120 13 ( ( PUNCT iajs-3911 120 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 120 15 ) ) PUNCT iajs-3911 120 16 2 2 NUM iajs-3911 120 17 𝑛 𝑛 PRON iajs-3911 120 18 𝑖=1 𝑖=1 PROPN iajs-3911 120 19 + + CCONJ iajs-3911 120 20 βˆ‘ βˆ‘ PROPN iajs-3911 120 21 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 120 22 ( ( PUNCT iajs-3911 120 23 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 120 24 ) ) PUNCT iajs-3911 120 25 3 3 NUM iajs-3911 120 26 𝑛 𝑛 PRON iajs-3911 120 27 𝑖=1 𝑖=1 PUNCT iajs-3911 120 28 βˆ‘ βˆ‘ PROPN iajs-3911 120 29 1 1 NUM iajs-3911 120 30 ( ( PUNCT iajs-3911 120 31 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 120 32 ) ) PUNCT iajs-3911 120 33 2 2 NUM iajs-3911 120 34 𝑛 𝑛 PRON iajs-3911 120 35 𝑖=1 𝑖=1 PROPN iajs-3911 120 36 ) ) PUNCT iajs-3911 121 1 + + CCONJ iajs-3911 121 2 1 1 NUM iajs-3911 121 3 βˆ‘ βˆ‘ NOUN iajs-3911 121 4 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 121 5 ( ( PUNCT iajs-3911 121 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 121 7 ) ) PUNCT iajs-3911 121 8 2 2 NUM iajs-3911 121 9 𝑛 𝑛 PRON iajs-3911 121 10 𝑖=1 𝑖=1 PROPN iajs-3911 122 1 ( ( PUNCT iajs-3911 122 2 βˆ‘ βˆ‘ PROPN iajs-3911 122 3 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 122 4 2 2 NUM iajs-3911 122 5 ( ( PUNCT iajs-3911 122 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 122 7 ) ) PUNCT iajs-3911 122 8 3 3 NUM iajs-3911 122 9 𝑛 𝑛 NOUN iajs-3911 122 10 𝑖=1 𝑖=1 PUNCT iajs-3911 122 11 βˆ‘ βˆ‘ PROPN iajs-3911 122 12 𝑑𝑖 𝑑𝑖 SYM iajs-3911 122 13 2 2 NUM iajs-3911 122 14 ( ( PUNCT iajs-3911 122 15 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 122 16 ) ) PUNCT iajs-3911 122 17 2 2 NUM iajs-3911 122 18 𝑛 𝑛 PRON iajs-3911 122 19 𝑖=1 𝑖=1 PROPN iajs-3911 123 1 + + CCONJ iajs-3911 123 2 βˆ‘ βˆ‘ PROPN iajs-3911 123 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 123 4 2 2 NUM iajs-3911 123 5 ( ( PUNCT iajs-3911 123 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 123 7 ) ) PUNCT iajs-3911 123 8 3 3 NUM iajs-3911 123 9 𝑛 𝑛 NOUN iajs-3911 123 10 𝑖=1 𝑖=1 PUNCT iajs-3911 123 11 βˆ‘ βˆ‘ ADV iajs-3911 123 12 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 123 13 ( ( PUNCT iajs-3911 123 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 123 15 ) ) PUNCT iajs-3911 123 16 2 2 NUM iajs-3911 123 17 𝑛 𝑛 PRON iajs-3911 123 18 𝑖=1 𝑖=1 PROPN iajs-3911 123 19 + + CCONJ iajs-3911 123 20 βˆ‘ βˆ‘ PROPN iajs-3911 123 21 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 123 22 ( ( PUNCT iajs-3911 123 23 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 123 24 ) ) PUNCT iajs-3911 123 25 3 3 NUM iajs-3911 123 26 𝑛 𝑛 NOUN iajs-3911 123 27 𝑖=1 𝑖=1 PUNCT iajs-3911 123 28 βˆ‘ βˆ‘ ADV iajs-3911 123 29 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 123 30 ( ( PUNCT iajs-3911 123 31 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 123 32 ) ) PUNCT iajs-3911 123 33 2 2 NUM iajs-3911 123 34 𝑛 𝑛 PRON iajs-3911 123 35 𝑖=1 𝑖=1 PROPN iajs-3911 124 1 + + CCONJ iajs-3911 124 2 βˆ‘ βˆ‘ SYM iajs-3911 124 3 1 1 NUM iajs-3911 124 4 ( ( PUNCT iajs-3911 124 5 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 124 6 ) ) PUNCT iajs-3911 124 7 3 3 NUM iajs-3911 124 8 𝑛 𝑛 PRON iajs-3911 124 9 𝑖=1 𝑖=1 PUNCT iajs-3911 124 10 βˆ‘ βˆ‘ PROPN iajs-3911 124 11 1 1 NUM iajs-3911 124 12 ( ( PUNCT iajs-3911 124 13 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 124 14 ) ) PUNCT iajs-3911 124 15 2 2 NUM iajs-3911 124 16 𝑛 𝑛 PRON iajs-3911 124 17 𝑖=1 𝑖=1 PROPN iajs-3911 124 18 ) ) PUNCT iajs-3911 124 19 ( ( PUNCT iajs-3911 124 20 22 22 NUM iajs-3911 124 21 ) ) PUNCT iajs-3911 124 22 2.4 2.4 NUM iajs-3911 124 23 . . PUNCT iajs-3911 125 1 tierney tierney PROPN iajs-3911 125 2 and and CCONJ iajs-3911 125 3 kadane kadane PROPN iajs-3911 125 4 approximation approximation NOUN iajs-3911 125 5 estimation estimation NOUN iajs-3911 125 6 method method NOUN iajs-3911 125 7 in in ADP iajs-3911 125 8 ( ( PUNCT iajs-3911 125 9 1986 1986 NUM iajs-3911 125 10 ) ) PUNCT iajs-3911 125 11 , , PUNCT iajs-3911 125 12 tierney tierney PROPN iajs-3911 125 13 and and CCONJ iajs-3911 125 14 kadane kadane VERB iajs-3911 125 15 the the DET iajs-3911 125 16 two two NUM iajs-3911 125 17 researchers researcher NOUN iajs-3911 125 18 used use VERB iajs-3911 125 19 an an DET iajs-3911 125 20 approximation approximation NOUN iajs-3911 125 21 method method NOUN iajs-3911 125 22 to to PART iajs-3911 125 23 calculate calculate VERB iajs-3911 125 24 the the DET iajs-3911 125 25 ratio ratio NOUN iajs-3911 125 26 of of ADP iajs-3911 125 27 integrals integral NOUN iajs-3911 125 28 and and CCONJ iajs-3911 125 29 according accord VERB iajs-3911 125 30 to to ADP iajs-3911 125 31 the the DET iajs-3911 125 32 following follow VERB iajs-3911 125 33 formula formula NOUN iajs-3911 125 34 ( ( PUNCT iajs-3911 125 35 28 28 NUM iajs-3911 125 36 ): ): PUNCT iajs-3911 125 37 βˆ«π‘€(πœƒ)𝑒𝐿(πœƒ)π‘‘πœƒ βˆ«π‘€(πœƒ)𝑒𝐿(πœƒ)π‘‘πœƒ PROPN iajs-3911 125 38 βˆ«π‘£(πœƒ)𝑒𝐿(πœƒ)π‘‘πœƒ βˆ«π‘£(πœƒ)𝑒𝐿(πœƒ)π‘‘πœƒ X iajs-3911 125 39 ( ( PUNCT iajs-3911 125 40 23 23 NUM iajs-3911 125 41 ) ) PUNCT iajs-3911 126 1 where where SCONJ iajs-3911 126 2 : : PUNCT iajs-3911 126 3 πœƒ πœƒ X iajs-3911 126 4 = = PUNCT iajs-3911 126 5 ( ( PUNCT iajs-3911 126 6 πœƒ1 πœƒ1 PROPN iajs-3911 126 7 , , PUNCT iajs-3911 126 8 πœƒ2 πœƒ2 PROPN iajs-3911 126 9 , , PUNCT iajs-3911 126 10 … … PUNCT iajs-3911 126 11 πœƒπ‘š πœƒπ‘š ADV iajs-3911 126 12 ): ): PUNCT iajs-3911 126 13 represents represent VERB iajs-3911 126 14 the the DET iajs-3911 126 15 vector vector NOUN iajs-3911 126 16 of of ADP iajs-3911 126 17 parameters parameter NOUN iajs-3911 126 18 , , PUNCT iajs-3911 126 19 to to PART iajs-3911 126 20 be be AUX iajs-3911 126 21 estimated.𝑀(πœƒ estimated.𝑀(πœƒ ADV iajs-3911 126 22 ) ) PUNCT iajs-3911 126 23 and and CCONJ iajs-3911 126 24 𝑣(πœƒ 𝑣(πœƒ NUM iajs-3911 126 25 ): ): PUNCT iajs-3911 126 26 are be AUX iajs-3911 126 27 optional optional ADJ iajs-3911 126 28 functions function NOUN iajs-3911 126 29 in in ADP iajs-3911 126 30 terms term NOUN iajs-3911 126 31 of of ADP iajs-3911 126 32 the the DET iajs-3911 126 33 parameters parameter NOUN iajs-3911 126 34 . . PUNCT iajs-3911 127 1 𝐿(πœƒ 𝐿(πœƒ X iajs-3911 127 2 ): ): PUNCT iajs-3911 127 3 logarithm logarithm NOUN iajs-3911 127 4 function function NOUN iajs-3911 127 5 of of ADP iajs-3911 127 6 the the DET iajs-3911 127 7 maximum maximum ADJ iajs-3911 127 8 likeihood likeihood NOUN iajs-3911 127 9 . . PUNCT iajs-3911 128 1 when when SCONJ iajs-3911 128 2 𝑣(πœƒ 𝑣(πœƒ VERB iajs-3911 128 3 ) ) PUNCT iajs-3911 128 4 is be AUX iajs-3911 128 5 the the DET iajs-3911 128 6 prior prior ADJ iajs-3911 128 7 density density NOUN iajs-3911 128 8 function function NOUN iajs-3911 128 9 of of ADP iajs-3911 128 10 parameters parameter NOUN iajs-3911 128 11 πœƒ πœƒ VERB iajs-3911 128 12 and and CCONJ iajs-3911 128 13 let let VERB iajs-3911 128 14 𝑀(πœƒ 𝑀(πœƒ VERB iajs-3911 128 15 ) ) PUNCT iajs-3911 128 16 = = SYM iajs-3911 129 1 πœ‘(πœƒ πœ‘(πœƒ PROPN iajs-3911 129 2 ) ) PUNCT iajs-3911 130 1 βˆ™ βˆ™ PROPN iajs-3911 130 2 𝑣(πœƒ 𝑣(πœƒ NUM iajs-3911 130 3 ) ) PUNCT iajs-3911 130 4 . . PUNCT iajs-3911 131 1 which which PRON iajs-3911 131 2 is be AUX iajs-3911 131 3 a a DET iajs-3911 131 4 function function NOUN iajs-3911 131 5 in in ADP iajs-3911 131 6 terms term NOUN iajs-3911 131 7 of of ADP iajs-3911 131 8 the the DET iajs-3911 131 9 parameter parameter NOUN iajs-3911 131 10 πœƒ πœƒ X iajs-3911 132 1 where where SCONJ iajs-3911 132 2 : : PUNCT iajs-3911 132 3 𝐸[πœ‘(πœƒ)|𝑑 𝐸[πœ‘(πœƒ)|𝑑 X iajs-3911 132 4 ] ] PUNCT iajs-3911 132 5 = = SYM iajs-3911 132 6 βˆ«πœ‘(πœƒ βˆ«πœ‘(πœƒ PROPN iajs-3911 132 7 ) ) PUNCT iajs-3911 132 8 𝑒(𝐿(πœƒ)+𝜌(πœƒ))π‘‘πœƒ 𝑒(𝐿(πœƒ)+𝜌(πœƒ))π‘‘πœƒ PROPN iajs-3911 132 9 ∫ ∫ PROPN iajs-3911 132 10 𝑒(𝐿(πœƒ)+𝜌(πœƒ))π‘‘πœƒ 𝑒(𝐿(πœƒ)+𝜌(πœƒ))π‘‘πœƒ PROPN iajs-3911 132 11 = = SYM iajs-3911 132 12 βˆ«πœ‘(πœƒ βˆ«πœ‘(πœƒ ADJ iajs-3911 132 13 ) ) PUNCT iajs-3911 132 14 𝑒(Ξ»(πœƒ))π‘‘πœƒ 𝑒(Ξ»(πœƒ))π‘‘πœƒ PROPN iajs-3911 132 15 ∫ ∫ PROPN iajs-3911 132 16 𝑒(Ξ»(πœƒ))π‘‘πœƒ 𝑒(Ξ»(πœƒ))π‘‘πœƒ PROPN iajs-3911 132 17 ( ( PUNCT iajs-3911 132 18 24 24 NUM iajs-3911 132 19 ) ) PUNCT iajs-3911 133 1 where where SCONJ iajs-3911 133 2 : : PUNCT iajs-3911 133 3 𝜌(πœƒ 𝜌(πœƒ NOUN iajs-3911 133 4 ) ) PUNCT iajs-3911 133 5 = = SYM iajs-3911 133 6 ln ln PROPN iajs-3911 133 7 𝜈(πœƒ 𝜈(πœƒ PROPN iajs-3911 133 8 ) ) PUNCT iajs-3911 133 9 , , PUNCT iajs-3911 133 10 Ξ»(πœƒ Ξ»(πœƒ PROPN iajs-3911 133 11 ) ) PUNCT iajs-3911 133 12 = = SYM iajs-3911 133 13 𝐿(πœƒ 𝐿(πœƒ X iajs-3911 133 14 ) ) PUNCT iajs-3911 133 15 + + NUM iajs-3911 133 16 𝜌(πœƒ 𝜌(πœƒ NOUN iajs-3911 133 17 ) ) PUNCT iajs-3911 133 18 = = SYM iajs-3911 133 19 𝐿(πœƒ 𝐿(πœƒ X iajs-3911 133 20 ) ) PUNCT iajs-3911 133 21 + + CCONJ iajs-3911 133 22 ln ln PROPN iajs-3911 133 23 𝜈(πœƒ 𝜈(πœƒ PROPN iajs-3911 133 24 ) ) PUNCT iajs-3911 133 25 tierney tierney PROPN iajs-3911 133 26 and and CCONJ iajs-3911 133 27 kadane kadane PROPN iajs-3911 133 28 were be AUX iajs-3911 133 29 managed manage VERB iajs-3911 133 30 to to PART iajs-3911 133 31 arrive arrive VERB iajs-3911 133 32 at at ADP iajs-3911 133 33 an an DET iajs-3911 133 34 estimate estimate NOUN iajs-3911 133 35 value value NOUN iajs-3911 133 36 𝐸[πœ‘(πœƒ)|𝑑 𝐸[πœ‘(πœƒ)|𝑑 NOUN iajs-3911 133 37 ] ] PUNCT iajs-3911 133 38 in in ADP iajs-3911 133 39 equation equation NOUN iajs-3911 133 40 ( ( PUNCT iajs-3911 133 41 24 24 NUM iajs-3911 133 42 ) ) PUNCT iajs-3911 133 43 by by ADP iajs-3911 133 44 using use VERB iajs-3911 133 45 taylor taylor PROPN iajs-3911 133 46 's 's PART iajs-3911 133 47 series series NOUN iajs-3911 133 48 to to PART iajs-3911 133 49 approximate approximate VERB iajs-3911 133 50 the the DET iajs-3911 133 51 maximum maximum NOUN iajs-3911 133 52 of of ADP iajs-3911 133 53 likeihood likeihood NOUN iajs-3911 133 54 the the DET iajs-3911 133 55 parameterπœƒ parameterπœƒ NOUN iajs-3911 133 56 , , PUNCT iajs-3911 133 57 using use VERB iajs-3911 133 58 independent independent ADJ iajs-3911 133 59 computations computation NOUN iajs-3911 133 60 for for ADP iajs-3911 133 61 the the DET iajs-3911 133 62 integration integration NOUN iajs-3911 133 63 of of ADP iajs-3911 133 64 the the DET iajs-3911 133 65 denominator denominator NOUN iajs-3911 133 66 and and CCONJ iajs-3911 133 67 the the DET iajs-3911 133 68 integration integration NOUN iajs-3911 133 69 of of ADP iajs-3911 133 70 the the DET iajs-3911 133 71 numerator numerator NOUN iajs-3911 133 72 separately separately ADV iajs-3911 133 73 and and CCONJ iajs-3911 133 74 then then ADV iajs-3911 133 75 the the DET iajs-3911 133 76 division division NOUN iajs-3911 133 77 of of ADP iajs-3911 133 78 the the DET iajs-3911 133 79 output output NOUN iajs-3911 133 80 ( ( PUNCT iajs-3911 133 81 29 29 NUM iajs-3911 133 82 ) ) PUNCT iajs-3911 133 83 , , PUNCT iajs-3911 133 84 taking take VERB iajs-3911 133 85 into into ADP iajs-3911 133 86 account account NOUN iajs-3911 133 87 the the DET iajs-3911 133 88 following follow VERB iajs-3911 133 89 two two NUM iajs-3911 133 90 possibilities possibility NOUN iajs-3911 133 91 : : PUNCT iajs-3911 133 92 Ο„ Ο„ X iajs-3911 133 93 = = PUNCT iajs-3911 133 94 𝐿(πœƒ 𝐿(πœƒ PROPN iajs-3911 133 95 𝑑⁄ 𝑑⁄ NUM iajs-3911 133 96 ) ) PUNCT iajs-3911 134 1 + + NUM iajs-3911 134 2 ln𝜈(πœƒ ln𝜈(πœƒ NOUN iajs-3911 134 3 ) ) PUNCT iajs-3911 134 4 𝑛 𝑛 PROPN iajs-3911 134 5 ( ( PUNCT iajs-3911 134 6 25 25 NUM iajs-3911 134 7 ) ) PUNCT iajs-3911 134 8 Ο„βˆ— Ο„βˆ— NOUN iajs-3911 134 9 = = SYM iajs-3911 134 10 𝑙𝑛 𝑙𝑛 PROPN iajs-3911 134 11 πœ‘(πœƒ)𝐿(πœƒ πœ‘(πœƒ)𝐿(πœƒ PROPN iajs-3911 134 12 𝑑⁄ 𝑑⁄ PROPN iajs-3911 134 13 ) ) PUNCT iajs-3911 135 1 + + ADJ iajs-3911 135 2 𝑙𝑛 𝑙𝑛 X iajs-3911 135 3 𝜈(πœƒ 𝜈(πœƒ PROPN iajs-3911 135 4 ) ) PUNCT iajs-3911 135 5 𝑛 𝑛 PROPN iajs-3911 135 6 ( ( PUNCT iajs-3911 135 7 26 26 NUM iajs-3911 135 8 ) ) PUNCT iajs-3911 135 9 find find VERB iajs-3911 135 10 the the DET iajs-3911 135 11 posterior posterior ADJ iajs-3911 135 12 distribution distribution NOUN iajs-3911 135 13 of of ADP iajs-3911 135 14 the the DET iajs-3911 135 15 function function NOUN iajs-3911 135 16 by by ADP iajs-3911 135 17 based base VERB iajs-3911 135 18 on on ADP iajs-3911 135 19 equation equation NOUN iajs-3911 135 20 ( ( PUNCT iajs-3911 135 21 25 25 NUM iajs-3911 135 22 ) ) PUNCT iajs-3911 135 23 and and CCONJ iajs-3911 135 24 ( ( PUNCT iajs-3911 135 25 26 26 NUM iajs-3911 135 26 ) ) PUNCT iajs-3911 135 27 , , PUNCT iajs-3911 135 28 then then ADV iajs-3911 135 29 the the DET iajs-3911 135 30 equation equation NOUN iajs-3911 135 31 ( ( PUNCT iajs-3911 135 32 24 24 NUM iajs-3911 135 33 ) ) PUNCT iajs-3911 135 34 becomes become VERB iajs-3911 135 35 as as SCONJ iajs-3911 135 36 follows follow VERB iajs-3911 135 37 : : PUNCT iajs-3911 135 38 𝐸[πœ‘(πœƒ)|𝑑 𝐸[πœ‘(πœƒ)|𝑑 X iajs-3911 135 39 ] ] PUNCT iajs-3911 135 40 = = PUNCT iajs-3911 136 1 βˆ«π‘’(π‘›Ο„βˆ—)π‘‘πœƒ βˆ«π‘’(π‘›Ο„βˆ—)π‘‘πœƒ SYM iajs-3911 136 2 ∫ ∫ PROPN iajs-3911 136 3 𝑒(nΟ„))π‘‘πœƒ 𝑒(nΟ„))π‘‘πœƒ PROPN iajs-3911 136 4 ( ( PUNCT iajs-3911 136 5 27 27 NUM iajs-3911 136 6 ) ) PUNCT iajs-3911 136 7 then then ADV iajs-3911 136 8 the the DET iajs-3911 136 9 approximate approximate ADJ iajs-3911 136 10 bayes bayes PROPN iajs-3911 136 11 estimator estimator NOUN iajs-3911 136 12 by by ADP iajs-3911 136 13 using use VERB iajs-3911 136 14 the the DET iajs-3911 136 15 tierney tierney NOUN iajs-3911 136 16 and and CCONJ iajs-3911 136 17 kadane kadane PROPN iajs-3911 136 18 method method NOUN iajs-3911 136 19 of of ADP iajs-3911 136 20 the the DET iajs-3911 136 21 function function NOUN iajs-3911 136 22 πœ™(πœƒ πœ™(πœƒ PROPN iajs-3911 136 23 ) ) PUNCT iajs-3911 136 24 is be AUX iajs-3911 136 25 as as SCONJ iajs-3911 136 26 follows follow VERB iajs-3911 136 27 : : PUNCT iajs-3911 136 28 οΏ½ οΏ½ PROPN iajs-3911 136 29 Μ‚ Μ‚ SYM iajs-3911 136 30 οΏ½ οΏ½ PROPN iajs-3911 136 31 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 NOUN iajs-3911 136 32 = = PUNCT iajs-3911 136 33 𝐸[πœ‘(πœƒ)|𝑑 𝐸[πœ‘(πœƒ)|𝑑 PROPN iajs-3911 136 34 ] ] X iajs-3911 136 35 = = PUNCT iajs-3911 136 36 [ [ PUNCT iajs-3911 136 37 |π»βˆ—| |π»βˆ—| NOUN iajs-3911 136 38 |𝐻| |𝐻| NOUN iajs-3911 136 39 ] ] SYM iajs-3911 136 40 1 1 NUM iajs-3911 136 41 2 2 NUM iajs-3911 136 42 exp exp NOUN iajs-3911 136 43 ( ( PUNCT iajs-3911 136 44 𝑛{π›΅βˆ—( 𝑛{π›΅βˆ—( NOUN iajs-3911 136 45 οΏ½ οΏ½ SYM iajs-3911 136 46 Μ‚ Μ‚ VERB iajs-3911 136 47 οΏ½ οΏ½ NOUN iajs-3911 136 48 βˆ— βˆ— NOUN iajs-3911 136 49 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NOUN iajs-3911 136 50 ) ) PUNCT iajs-3911 136 51 βˆ’ βˆ’ PROPN iajs-3911 136 52 𝑇 𝑇 PROPN iajs-3911 136 53 ( ( PUNCT iajs-3911 136 54 οΏ½ οΏ½ PROPN iajs-3911 136 55 Μ‚ Μ‚ NOUN iajs-3911 136 56 οΏ½ οΏ½ NOUN iajs-3911 136 57 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NUM iajs-3911 136 58 ) ) PUNCT iajs-3911 136 59 } } PUNCT iajs-3911 136 60 ) ) PUNCT iajs-3911 136 61 ( ( PUNCT iajs-3911 136 62 28 28 NUM iajs-3911 136 63 ) ) PUNCT iajs-3911 136 64 where where SCONJ iajs-3911 136 65 : : PUNCT iajs-3911 136 66 οΏ½ οΏ½ PROPN iajs-3911 136 67 Μ‚ Μ‚ PROPN iajs-3911 136 68 οΏ½ οΏ½ PROPN iajs-3911 136 69 𝐡𝑦𝑠𝑒(𝑑 𝐡𝑦𝑠𝑒(𝑑 NOUN iajs-3911 136 70 ): ): PUNCT iajs-3911 136 71 estimation estimation NOUN iajs-3911 136 72 of of ADP iajs-3911 136 73 the the DET iajs-3911 136 74 function function NOUN iajs-3911 136 75 πœ™(πœƒ πœ™(πœƒ PROPN iajs-3911 136 76 ) ) PUNCT iajs-3911 136 77 based base VERB iajs-3911 136 78 on on ADP iajs-3911 136 79 the the DET iajs-3911 136 80 method method NOUN iajs-3911 136 81 of of ADP iajs-3911 136 82 researchers researcher NOUN iajs-3911 136 83 tierney tierney PROPN iajs-3911 136 84 and and CCONJ iajs-3911 136 85 kadane kadane PROPN iajs-3911 136 86 πœƒ πœƒ PROPN iajs-3911 136 87 , , PUNCT iajs-3911 136 88 πœƒβˆ— πœƒβˆ— PROPN iajs-3911 136 89 : : PUNCT iajs-3911 136 90 the the DET iajs-3911 136 91 values value NOUN iajs-3911 136 92 that that PRON iajs-3911 136 93 maximize maximize VERB iajs-3911 136 94 Ο„ Ο„ PROPN iajs-3911 136 95 and and CCONJ iajs-3911 136 96 Ο„βˆ— Ο„βˆ— NOUN iajs-3911 136 97 respectively respectively ADV iajs-3911 136 98 . . PUNCT iajs-3911 137 1 𝐻,π»βˆ— 𝐻,π»βˆ— NUM iajs-3911 137 2 : : PUNCT iajs-3911 137 3 negative negative ADJ iajs-3911 137 4 inverse inverse NOUN iajs-3911 137 5 matrix matrix NOUN iajs-3911 137 6 hessian hessian NOUN iajs-3911 137 7 for for ADP iajs-3911 137 8 both both PRON iajs-3911 137 9 , , PUNCT iajs-3911 137 10 Ο„ Ο„ PROPN iajs-3911 137 11 , , PUNCT iajs-3911 137 12 Ο„βˆ—at Ο„βˆ—at NUM iajs-3911 137 13 πœƒand πœƒand NOUN iajs-3911 137 14 πœƒβˆ— πœƒβˆ— PROPN iajs-3911 137 15 respectively respectively ADV iajs-3911 137 16 of of ADP iajs-3911 137 17 class class NOUN iajs-3911 137 18 π‘š π‘š PROPN iajs-3911 137 19 Γ— Γ— PROPN iajs-3911 137 20 π‘š π‘š NOUN iajs-3911 137 21 , , PUNCT iajs-3911 137 22 π‘š π‘š ADP iajs-3911 137 23 the the DET iajs-3911 137 24 number number NOUN iajs-3911 137 25 of of ADP iajs-3911 137 26 parameters parameter NOUN iajs-3911 137 27 to to PART iajs-3911 137 28 be be AUX iajs-3911 137 29 estimated estimate VERB iajs-3911 137 30 . . PUNCT iajs-3911 138 1 as as ADP iajs-3911 138 2 a a DET iajs-3911 138 3 result result NOUN iajs-3911 138 4 , , PUNCT iajs-3911 138 5 it it PRON iajs-3911 138 6 needs need VERB iajs-3911 138 7 to to PART iajs-3911 138 8 find find VERB iajs-3911 138 9 values value NOUN iajs-3911 138 10 t t NOUN iajs-3911 138 11 and and CCONJ iajs-3911 138 12 Ο„βˆ— Ο„βˆ— NOUN iajs-3911 138 13 in in ADP iajs-3911 138 14 equations equation NOUN iajs-3911 138 15 ( ( PUNCT iajs-3911 138 16 25 25 NUM iajs-3911 138 17 , , PUNCT iajs-3911 138 18 26 26 NUM iajs-3911 138 19 ) ) PUNCT iajs-3911 138 20 as as SCONJ iajs-3911 138 21 follows follow VERB iajs-3911 138 22 : : PUNCT iajs-3911 138 23 Ο„ Ο„ PROPN iajs-3911 138 24 = = SYM iajs-3911 138 25 ln[β„Ž(πœƒ;𝑑1,𝑑2, ln[β„Ž(πœƒ;𝑑1,𝑑2, NOUN iajs-3911 138 26 … … SYM iajs-3911 138 27 ,𝑑𝑛 ,𝑑𝑛 NUM iajs-3911 138 28 ) ) PUNCT iajs-3911 138 29 ] ] PUNCT iajs-3911 139 1 𝑛 𝑛 PROPN iajs-3911 139 2 ( ( PUNCT iajs-3911 139 3 29 29 NUM iajs-3911 139 4 ) ) PUNCT iajs-3911 139 5 Ο„βˆ— Ο„βˆ— NOUN iajs-3911 139 6 = = SYM iajs-3911 139 7 ln[πœ™(πœƒ)β„Ž(πœƒ;𝑑1,𝑑2, ln[πœ™(πœƒ)β„Ž(πœƒ;𝑑1,𝑑2, PROPN iajs-3911 139 8 … … PUNCT iajs-3911 139 9 ,𝑑𝑛 ,𝑑𝑛 X iajs-3911 139 10 ) ) PUNCT iajs-3911 139 11 ] ] PUNCT iajs-3911 140 1 𝑛 𝑛 X iajs-3911 140 2 ( ( PUNCT iajs-3911 140 3 30 30 NUM iajs-3911 140 4 ) ) PUNCT iajs-3911 140 5 ihjpas ihjpa NOUN iajs-3911 140 6 . . PUNCT iajs-3911 141 1 2025,38(2 2025,38(2 NOUN iajs-3911 141 2 ) ) PUNCT iajs-3911 141 3 408 408 NUM iajs-3911 141 4 estimation estimation NOUN iajs-3911 141 5 of of ADP iajs-3911 141 6 parameter parameter NOUN iajs-3911 141 7 ( ( PUNCT iajs-3911 141 8 𝛼)when 𝛼)when PROPN iajs-3911 141 9 the the DET iajs-3911 141 10 parameter parameter NOUN iajs-3911 141 11 ( ( PUNCT iajs-3911 141 12 πœ† πœ† X iajs-3911 141 13 ) ) PUNCT iajs-3911 141 14 is be AUX iajs-3911 141 15 knows know VERB iajs-3911 141 16 . . PUNCT iajs-3911 142 1 assume assume VERB iajs-3911 142 2 that that SCONJ iajs-3911 142 3 πœ™(𝛼 πœ™(𝛼 NOUN iajs-3911 142 4 , , PUNCT iajs-3911 142 5 πœ† πœ† NOUN iajs-3911 142 6 ) ) PUNCT iajs-3911 142 7 = = SYM iajs-3911 142 8 𝛼 𝛼 X iajs-3911 142 9 in in ADP iajs-3911 142 10 equation equation NOUN iajs-3911 142 11 ( ( PUNCT iajs-3911 142 12 27 27 NUM iajs-3911 142 13 ) ) PUNCT iajs-3911 142 14 and and CCONJ iajs-3911 142 15 then then ADV iajs-3911 142 16 οΏ½ οΏ½ PROPN iajs-3911 142 17 Μ‚ Μ‚ SYM iajs-3911 142 18 οΏ½ οΏ½ PROPN iajs-3911 142 19 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 PROPN iajs-3911 142 20 = = SYM iajs-3911 142 21 𝐸(𝛼|𝑑 𝐸(𝛼|𝑑 PROPN iajs-3911 142 22 ) ) PUNCT iajs-3911 142 23 . . PUNCT iajs-3911 143 1 where where SCONJ iajs-3911 143 2 οΏ½ οΏ½ PROPN iajs-3911 143 3 Μ‚ Μ‚ SYM iajs-3911 143 4 οΏ½ οΏ½ PROPN iajs-3911 143 5 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 PROPN iajs-3911 143 6 denote denote VERB iajs-3911 143 7 the the DET iajs-3911 143 8 bayes bayes PROPN iajs-3911 143 9 estimator estimator NOUN iajs-3911 143 10 of of ADP iajs-3911 143 11 𝛼 𝛼 NOUN iajs-3911 143 12 according accord VERB iajs-3911 143 13 to to ADP iajs-3911 143 14 tierney tierney PROPN iajs-3911 143 15 and and CCONJ iajs-3911 143 16 kadane kadane PROPN iajs-3911 143 17 approximation approximation NOUN iajs-3911 143 18 . . PUNCT iajs-3911 144 1 then then ADV iajs-3911 144 2 οΏ½ οΏ½ PROPN iajs-3911 144 3 Μ‚ Μ‚ SYM iajs-3911 144 4 οΏ½ οΏ½ PROPN iajs-3911 144 5 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 PROPN iajs-3911 144 6 = = SYM iajs-3911 144 7 ∫ ∫ PROPN iajs-3911 144 8 πœ™(𝛼 πœ™(𝛼 X iajs-3911 144 9 ) ) PUNCT iajs-3911 144 10 𝑒ι(𝛼,πœ† 𝑒ι(𝛼,πœ† PUNCT iajs-3911 144 11 ) ) PUNCT iajs-3911 145 1 𝑒ln(𝑣)𝑑𝛼 𝑒ln(𝑣)𝑑𝛼 NUM iajs-3911 146 1 ∞ ∞ NUM iajs-3911 146 2 0 0 NUM iajs-3911 147 1 ∫ ∫ PROPN iajs-3911 147 2 𝑒ι(𝛼,πœ†)𝑒ln(𝑣)𝑑𝛼 𝑒ι(𝛼,πœ†)𝑒ln(𝑣)𝑑𝛼 PROPN iajs-3911 148 1 ∞ ∞ PROPN iajs-3911 148 2 0 0 NUM iajs-3911 149 1 = = SYM iajs-3911 149 2 ∫ ∫ X iajs-3911 149 3 πœ™(𝛼 πœ™(𝛼 X iajs-3911 149 4 ) ) PUNCT iajs-3911 149 5 𝑒ι(𝛼,πœ† 𝑒ι(𝛼,πœ† NOUN iajs-3911 149 6 ) ) PUNCT iajs-3911 149 7 𝑣 𝑣 ADP iajs-3911 149 8 𝑑𝛼 𝑑𝛼 NOUN iajs-3911 149 9 ∞ ∞ PROPN iajs-3911 149 10 0 0 NUM iajs-3911 149 11 ∫ ∫ PROPN iajs-3911 149 12 𝑒ι(𝛼,πœ† 𝑒ι(𝛼,πœ† NUM iajs-3911 149 13 ) ) PUNCT iajs-3911 150 1 𝑣 𝑣 ADP iajs-3911 150 2 𝑑𝛼 𝑑𝛼 NOUN iajs-3911 150 3 ∞ ∞ PROPN iajs-3911 150 4 0 0 NUM iajs-3911 150 5 , , PUNCT iajs-3911 150 6 where where SCONJ iajs-3911 150 7 𝑣 𝑣 ADP iajs-3911 150 8 = = SYM iajs-3911 150 9 𝑔1(𝛼 𝑔1(𝛼 PROPN iajs-3911 150 10 ) ) PUNCT iajs-3911 150 11 οΏ½ οΏ½ PROPN iajs-3911 150 12 Μ‚ Μ‚ SYM iajs-3911 150 13 οΏ½ οΏ½ NOUN iajs-3911 150 14 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 NOUN iajs-3911 150 15 = = PUNCT iajs-3911 150 16 πœƒ πœƒ X iajs-3911 150 17 𝑒 𝑒 PROPN iajs-3911 150 18 βˆ’ βˆ’ NOUN iajs-3911 150 19 πœ† πœ† SYM iajs-3911 150 20 2 2 NUM iajs-3911 150 21 βˆ‘ βˆ‘ PROPN iajs-3911 150 22 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 150 23 2𝑛 2𝑛 PROPN iajs-3911 150 24 𝑖=1 𝑖=1 PROPN iajs-3911 150 25 ∫ ∫ PROPN iajs-3911 150 26 𝛼 𝛼 PROPN iajs-3911 150 27 ∏ ∏ PROPN iajs-3911 150 28 ( ( PUNCT iajs-3911 150 29 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– X iajs-3911 150 30 ) ) PUNCT iajs-3911 150 31 𝑒 𝑒 PROPN iajs-3911 150 32 βˆ’π›Ό βˆ’π›Ό PROPN iajs-3911 150 33 βˆ‘ βˆ‘ PUNCT iajs-3911 150 34 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 150 35 𝑛 𝑛 PROPN iajs-3911 150 36 𝑖=1𝑛 𝑖=1𝑛 NOUN iajs-3911 150 37 𝑖=1 𝑖=1 PROPN iajs-3911 150 38 π‘’βˆ’πœƒπ›Ό π‘’βˆ’πœƒπ›Ό PROPN iajs-3911 150 39 𝑑𝛼 𝑑𝛼 NOUN iajs-3911 150 40 ∞ ∞ PROPN iajs-3911 150 41 0 0 PUNCT iajs-3911 151 1 πœƒ πœƒ PRON iajs-3911 151 2 𝑒 𝑒 PROPN iajs-3911 151 3 βˆ’ βˆ’ NOUN iajs-3911 151 4 πœ† πœ† SYM iajs-3911 151 5 2 2 NUM iajs-3911 151 6 βˆ‘ βˆ‘ PROPN iajs-3911 151 7 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 151 8 2𝑛 2𝑛 PROPN iajs-3911 151 9 𝑖=1 𝑖=1 PROPN iajs-3911 152 1 ∫ ∫ PROPN iajs-3911 152 2 ∏ ∏ PROPN iajs-3911 152 3 ( ( PUNCT iajs-3911 152 4 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– X iajs-3911 152 5 ) ) PUNCT iajs-3911 152 6 𝑒 𝑒 PROPN iajs-3911 152 7 βˆ’π›Όβˆ‘ βˆ’π›Όβˆ‘ PROPN iajs-3911 152 8 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 152 9 𝑛 𝑛 PROPN iajs-3911 152 10 𝑖=1𝑛 𝑖=1𝑛 NOUN iajs-3911 152 11 𝑖=1 𝑖=1 PROPN iajs-3911 153 1 π‘’βˆ’πœƒπ›Ό π‘’βˆ’πœƒπ›Ό PROPN iajs-3911 153 2 𝑑𝛼 𝑑𝛼 NOUN iajs-3911 153 3 ∞ ∞ PROPN iajs-3911 153 4 0 0 PUNCT iajs-3911 154 1 ( ( PUNCT iajs-3911 154 2 31 31 NUM iajs-3911 154 3 ) ) PUNCT iajs-3911 155 1 so so ADV iajs-3911 155 2 Ο„ Ο„ PROPN iajs-3911 155 3 = = PUNCT iajs-3911 155 4 𝑙𝑛 𝑙𝑛 NOUN iajs-3911 155 5 𝑛 𝑛 PROPN iajs-3911 156 1 [ [ X iajs-3911 156 2 ∏ ∏ X iajs-3911 156 3 ( ( PUNCT iajs-3911 156 4 𝛼 𝛼 NOUN iajs-3911 156 5 + + NUM iajs-3911 156 6 πœ†π‘‘π‘– πœ†π‘‘π‘– NOUN iajs-3911 156 7 ) ) PUNCT iajs-3911 156 8 𝑒 𝑒 PROPN iajs-3911 156 9 βˆ’π›Ό βˆ’π›Ό PROPN iajs-3911 156 10 βˆ‘ βˆ‘ PUNCT iajs-3911 156 11 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 156 12 𝑛 𝑛 PROPN iajs-3911 156 13 𝑖=1𝑛 𝑖=1𝑛 NOUN iajs-3911 156 14 𝑖=1 𝑖=1 PROPN iajs-3911 156 15 π‘’βˆ’πœƒπ›Ό π‘’βˆ’πœƒπ›Ό PROPN iajs-3911 156 16 ] ] X iajs-3911 156 17 = = PUNCT iajs-3911 156 18 βˆ‘ βˆ‘ PUNCT iajs-3911 156 19 ln(𝛼+πœ†π‘‘π‘– ln(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 156 20 ) ) PUNCT iajs-3911 156 21 𝑛 𝑛 PROPN iajs-3911 156 22 𝑖=1 𝑖=1 PUNCT iajs-3911 157 1 𝑛 𝑛 DET iajs-3911 157 2 βˆ’ βˆ’ NOUN iajs-3911 157 3 𝛼 𝛼 INTJ iajs-3911 157 4 βˆ‘ βˆ‘ PROPN iajs-3911 157 5 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 157 6 𝑛 𝑛 PROPN iajs-3911 157 7 𝑖=1 𝑖=1 PUNCT iajs-3911 157 8 𝑛 𝑛 DET iajs-3911 157 9 βˆ’ βˆ’ PROPN iajs-3911 157 10 πœƒπ›Ό πœƒπ›Ό VERB iajs-3911 157 11 𝑛 𝑛 PROPN iajs-3911 157 12 ( ( PUNCT iajs-3911 157 13 32 32 NUM iajs-3911 157 14 ) ) PUNCT iajs-3911 157 15 Ο„βˆ— Ο„βˆ— NOUN iajs-3911 157 16 = = PUNCT iajs-3911 157 17 𝑙𝑛 𝑙𝑛 NOUN iajs-3911 157 18 𝑛 𝑛 PROPN iajs-3911 158 1 [ [ X iajs-3911 158 2 𝛼 𝛼 X iajs-3911 158 3 ∏ ∏ PROPN iajs-3911 158 4 ( ( PUNCT iajs-3911 158 5 𝛼 𝛼 NOUN iajs-3911 158 6 + + NUM iajs-3911 158 7 πœ†π‘‘π‘– πœ†π‘‘π‘– NOUN iajs-3911 158 8 ) ) PUNCT iajs-3911 158 9 𝑒 𝑒 PROPN iajs-3911 158 10 βˆ’π›Ό βˆ’π›Ό PROPN iajs-3911 158 11 βˆ‘ βˆ‘ PUNCT iajs-3911 158 12 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 158 13 𝑛 𝑛 PROPN iajs-3911 158 14 𝑖=1𝑛 𝑖=1𝑛 NOUN iajs-3911 158 15 𝑖=1 𝑖=1 PROPN iajs-3911 158 16 π‘’βˆ’πœƒπ›Ό π‘’βˆ’πœƒπ›Ό PROPN iajs-3911 158 17 ] ] X iajs-3911 158 18 = = SYM iajs-3911 158 19 ln(𝛼 ln(𝛼 X iajs-3911 158 20 ) ) PUNCT iajs-3911 158 21 𝑛 𝑛 PROPN iajs-3911 158 22 + + ADJ iajs-3911 158 23 βˆ‘ βˆ‘ PROPN iajs-3911 158 24 ln(𝛼+πœ†π‘‘π‘– ln(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 158 25 ) ) PUNCT iajs-3911 158 26 𝑛 𝑛 PROPN iajs-3911 158 27 𝑖=1 𝑖=1 PUNCT iajs-3911 159 1 𝑛 𝑛 DET iajs-3911 159 2 βˆ’ βˆ’ NOUN iajs-3911 159 3 𝛼 𝛼 INTJ iajs-3911 159 4 βˆ‘ βˆ‘ PROPN iajs-3911 159 5 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 159 6 𝑛 𝑛 PROPN iajs-3911 159 7 𝑖=1 𝑖=1 PUNCT iajs-3911 159 8 𝑛 𝑛 DET iajs-3911 159 9 βˆ’ βˆ’ PROPN iajs-3911 159 10 πœƒπ›Ό πœƒπ›Ό VERB iajs-3911 159 11 𝑛 𝑛 PROPN iajs-3911 159 12 ( ( PUNCT iajs-3911 159 13 33 33 NUM iajs-3911 159 14 ) ) PUNCT iajs-3911 159 15 to to PART iajs-3911 159 16 find find VERB iajs-3911 159 17 π›Όπ‘šπ‘Žπ‘₯ π›Όπ‘šπ‘Žπ‘₯ NOUN iajs-3911 159 18 and and CCONJ iajs-3911 159 19 π›Όβˆ— π›Όβˆ— PROPN iajs-3911 159 20 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ PRON iajs-3911 159 21 which which PRON iajs-3911 159 22 are be AUX iajs-3911 159 23 the the DET iajs-3911 159 24 values value NOUN iajs-3911 159 25 that that PRON iajs-3911 159 26 maximize maximize VERB iajs-3911 159 27 Ο„ Ο„ PROPN iajs-3911 159 28 and and CCONJ iajs-3911 159 29 Ο„βˆ—respectively Ο„βˆ—respectively ADV iajs-3911 159 30 : : PUNCT iajs-3911 159 31 πœ•Ο„ πœ•Ο„ ADJ iajs-3911 159 32 πœ•π›Ό πœ•π›Ό NOUN iajs-3911 159 33 = = SYM iajs-3911 159 34 1 1 NUM iajs-3911 159 35 𝑛 𝑛 PROPN iajs-3911 159 36 βˆ‘ βˆ‘ ADP iajs-3911 159 37 1 1 NUM iajs-3911 159 38 ( ( PUNCT iajs-3911 159 39 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 159 40 ) ) PUNCT iajs-3911 159 41 𝑛 𝑛 PRON iajs-3911 159 42 𝑖=1 𝑖=1 PUNCT iajs-3911 159 43 βˆ’ βˆ’ PROPN iajs-3911 159 44 βˆ‘ βˆ‘ PROPN iajs-3911 159 45 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 159 46 𝑛 𝑛 PROPN iajs-3911 159 47 𝑖=1 𝑖=1 PUNCT iajs-3911 159 48 𝑛 𝑛 DET iajs-3911 159 49 βˆ’ βˆ’ PROPN iajs-3911 159 50 πœƒ πœƒ NOUN iajs-3911 159 51 𝑛 𝑛 DET iajs-3911 159 52 πœ•Ο„βˆ— πœ•Ο„βˆ— PROPN iajs-3911 159 53 πœ•π›Ό πœ•π›Ό NOUN iajs-3911 159 54 = = NOUN iajs-3911 159 55 1 1 NUM iajs-3911 159 56 𝑛𝛼 𝑛𝛼 NOUN iajs-3911 159 57 + + PROPN iajs-3911 159 58 1 1 NUM iajs-3911 159 59 𝑛 𝑛 PRON iajs-3911 159 60 βˆ‘ βˆ‘ ADP iajs-3911 159 61 1 1 NUM iajs-3911 159 62 ( ( PUNCT iajs-3911 159 63 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 159 64 ) ) PUNCT iajs-3911 159 65 𝑛 𝑛 PRON iajs-3911 159 66 𝑖=1 𝑖=1 PUNCT iajs-3911 159 67 βˆ’ βˆ’ PROPN iajs-3911 159 68 βˆ‘ βˆ‘ PROPN iajs-3911 159 69 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 159 70 𝑛 𝑛 PROPN iajs-3911 159 71 𝑖=1 𝑖=1 PUNCT iajs-3911 159 72 𝑛 𝑛 PRON iajs-3911 159 73 βˆ’ βˆ’ NOUN iajs-3911 159 74 πœƒ πœƒ NUM iajs-3911 159 75 𝑛 𝑛 DET iajs-3911 159 76 οΏ½ οΏ½ PROPN iajs-3911 159 77 Μ‚ Μ‚ NOUN iajs-3911 159 78 οΏ½ οΏ½ NOUN iajs-3911 159 79 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ VERB iajs-3911 159 80 = = SYM iajs-3911 159 81 βˆ‘ βˆ‘ PROPN iajs-3911 159 82 1 1 NUM iajs-3911 159 83 ( ( PUNCT iajs-3911 159 84 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 159 85 ) ) PUNCT iajs-3911 159 86 𝑛 𝑛 PRON iajs-3911 159 87 𝑖=1 𝑖=1 PUNCT iajs-3911 159 88 βˆ’ βˆ’ PROPN iajs-3911 159 89 βˆ‘ βˆ‘ PROPN iajs-3911 159 90 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 159 91 𝑛 𝑛 PROPN iajs-3911 159 92 𝑖=1 𝑖=1 PROPN iajs-3911 159 93 βˆ’ βˆ’ PROPN iajs-3911 159 94 πœƒ πœƒ SYM iajs-3911 159 95 οΏ½ οΏ½ PROPN iajs-3911 159 96 Μ‚ Μ‚ NOUN iajs-3911 159 97 οΏ½ οΏ½ NOUN iajs-3911 159 98 βˆ— βˆ— NOUN iajs-3911 159 99 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ VERB iajs-3911 159 100 = = SYM iajs-3911 159 101 1 1 NUM iajs-3911 159 102 𝛼 𝛼 NOUN iajs-3911 159 103 + + NOUN iajs-3911 159 104 βˆ‘ βˆ‘ PROPN iajs-3911 159 105 1 1 NUM iajs-3911 159 106 ( ( PUNCT iajs-3911 159 107 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 159 108 ) ) PUNCT iajs-3911 159 109 𝑛 𝑛 PRON iajs-3911 159 110 𝑖=1 𝑖=1 PUNCT iajs-3911 159 111 βˆ’ βˆ’ PROPN iajs-3911 159 112 βˆ‘ βˆ‘ PROPN iajs-3911 159 113 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 159 114 𝑛 𝑛 PROPN iajs-3911 159 115 𝑖=1 𝑖=1 PROPN iajs-3911 159 116 βˆ’ βˆ’ PROPN iajs-3911 159 117 πœƒ πœƒ SYM iajs-3911 159 118 οΏ½ οΏ½ PROPN iajs-3911 159 119 Μ‚ Μ‚ NOUN iajs-3911 159 120 οΏ½ οΏ½ NOUN iajs-3911 159 121 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ ADJ iajs-3911 159 122 and and CCONJ iajs-3911 159 123 οΏ½ οΏ½ PROPN iajs-3911 159 124 Μ‚ Μ‚ NOUN iajs-3911 159 125 οΏ½ οΏ½ NOUN iajs-3911 159 126 βˆ— βˆ— NOUN iajs-3911 159 127 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NOUN iajs-3911 159 128 are be AUX iajs-3911 159 129 maximum maximum ADJ iajs-3911 159 130 since since SCONJ iajs-3911 159 131 : : PUNCT iajs-3911 159 132 πœ•2Ο„ πœ•2Ο„ NUM iajs-3911 159 133 πœ•2𝛼 πœ•2𝛼 PROPN iajs-3911 160 1 = = SYM iajs-3911 160 2 βˆ’1 βˆ’1 NOUN iajs-3911 160 3 𝑛 𝑛 PROPN iajs-3911 160 4 βˆ‘ βˆ‘ PROPN iajs-3911 160 5 1 1 NUM iajs-3911 160 6 ( ( PUNCT iajs-3911 160 7 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 160 8 ) ) PUNCT iajs-3911 160 9 2 2 NUM iajs-3911 160 10 𝑛 𝑛 PRON iajs-3911 160 11 𝑖=1 𝑖=1 PUNCT iajs-3911 160 12 < < X iajs-3911 160 13 0 0 NUM iajs-3911 160 14 πœ•2Ο„βˆ— πœ•2Ο„βˆ— X iajs-3911 160 15 πœ•2𝛼 πœ•2𝛼 PROPN iajs-3911 160 16 = = SYM iajs-3911 160 17 βˆ’1 βˆ’1 NOUN iajs-3911 160 18 𝑛 𝑛 PROPN iajs-3911 160 19 ( ( PUNCT iajs-3911 160 20 1 1 NUM iajs-3911 160 21 𝛼2 𝛼2 ADJ iajs-3911 160 22 + + CCONJ iajs-3911 160 23 βˆ‘ βˆ‘ PROPN iajs-3911 160 24 1 1 NUM iajs-3911 160 25 ( ( PUNCT iajs-3911 160 26 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 160 27 ) ) PUNCT iajs-3911 160 28 2 2 NUM iajs-3911 160 29 𝑛 𝑛 PRON iajs-3911 160 30 𝑖=1 𝑖=1 PUNCT iajs-3911 160 31 ) ) PUNCT iajs-3911 161 1 < < X iajs-3911 161 2 0 0 NUM iajs-3911 161 3 necessary necessary ADJ iajs-3911 161 4 and and CCONJ iajs-3911 161 5 sufficient sufficient ADJ iajs-3911 161 6 is be AUX iajs-3911 161 7 that that DET iajs-3911 161 8 second second ADJ iajs-3911 161 9 derivate derivate NOUN iajs-3911 161 10 respect respect NOUN iajs-3911 161 11 to to ADP iajs-3911 161 12 𝛼 𝛼 PROPN iajs-3911 161 13 is be AUX iajs-3911 161 14 negative negative ADJ iajs-3911 161 15 ( ( PUNCT iajs-3911 161 16 30 30 NUM iajs-3911 161 17 ) ) PUNCT iajs-3911 161 18 . . PUNCT iajs-3911 162 1 the the DET iajs-3911 162 2 determinant determinant NOUN iajs-3911 162 3 of of ADP iajs-3911 162 4 the the DET iajs-3911 162 5 negative negative NOUN iajs-3911 162 6 of of ADP iajs-3911 162 7 the the DET iajs-3911 162 8 inverse inverse NOUN iajs-3911 162 9 hessian hessian NOUN iajs-3911 162 10 of of ADP iajs-3911 162 11 Ο„ Ο„ PROPN iajs-3911 162 12 at at ADP iajs-3911 162 13 οΏ½ οΏ½ PROPN iajs-3911 162 14 Μ‚ Μ‚ SYM iajs-3911 162 15 οΏ½ οΏ½ NOUN iajs-3911 162 16 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NOUN iajs-3911 162 17 and and CCONJ iajs-3911 162 18 Ο„βˆ— Ο„βˆ— NOUN iajs-3911 162 19 at at ADP iajs-3911 162 20 οΏ½ οΏ½ PROPN iajs-3911 162 21 Μ‚ Μ‚ NOUN iajs-3911 162 22 οΏ½ οΏ½ NOUN iajs-3911 162 23 βˆ— βˆ— NOUN iajs-3911 162 24 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ PRON iajs-3911 162 25 respectively respectively ADV iajs-3911 162 26 : : PUNCT iajs-3911 162 27 𝐻 𝐻 PROPN iajs-3911 162 28 = = SYM iajs-3911 162 29 βˆ’ βˆ’ PROPN iajs-3911 162 30 [ [ PUNCT iajs-3911 162 31 πœ•2Ο„ πœ•2Ο„ NOUN iajs-3911 162 32 πœ•2𝛼 πœ•2𝛼 PROPN iajs-3911 162 33 ] ] PUNCT iajs-3911 162 34 βˆ’1 βˆ’1 NOUN iajs-3911 162 35 𝛼=π›Όπ‘šπ‘Žπ‘₯ 𝛼=π›Όπ‘šπ‘Žπ‘₯ NUM iajs-3911 162 36 = = SYM iajs-3911 162 37 βˆ’ βˆ’ PROPN iajs-3911 162 38 [ [ PUNCT iajs-3911 162 39 βˆ’1 βˆ’1 NOUN iajs-3911 162 40 𝑛 𝑛 PROPN iajs-3911 162 41 βˆ‘ βˆ‘ PROPN iajs-3911 162 42 1 1 NUM iajs-3911 162 43 ( ( PUNCT iajs-3911 162 44 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 162 45 ) ) PUNCT iajs-3911 162 46 2 2 NUM iajs-3911 162 47 𝑛 𝑛 PRON iajs-3911 162 48 𝑖=1 𝑖=1 PROPN iajs-3911 162 49 ] ] PUNCT iajs-3911 162 50 βˆ’1 βˆ’1 NOUN iajs-3911 162 51 = = SYM iajs-3911 162 52 𝑛 𝑛 PRON iajs-3911 162 53 βˆ‘ βˆ‘ PROPN iajs-3911 162 54 1 1 NUM iajs-3911 162 55 ( ( PUNCT iajs-3911 162 56 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 162 57 ) ) PUNCT iajs-3911 162 58 2 2 NUM iajs-3911 162 59 𝑛 𝑛 PROPN iajs-3911 162 60 𝑖=1 𝑖=1 PROPN iajs-3911 162 61 ( ( PUNCT iajs-3911 162 62 34 34 NUM iajs-3911 162 63 ) ) PUNCT iajs-3911 162 64 π»βˆ— π»βˆ— NOUN iajs-3911 162 65 = = SYM iajs-3911 162 66 βˆ’ βˆ’ PROPN iajs-3911 162 67 [ [ PUNCT iajs-3911 162 68 πœ•2π›΅βˆ— πœ•2π›΅βˆ— NUM iajs-3911 162 69 πœ•2𝛼 πœ•2𝛼 PROPN iajs-3911 162 70 ] ] PUNCT iajs-3911 162 71 βˆ’1 βˆ’1 NOUN iajs-3911 162 72 𝛼=π›Όβˆ— 𝛼=π›Όβˆ— X iajs-3911 162 73 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ ADJ iajs-3911 162 74 = = SYM iajs-3911 162 75 βˆ’ βˆ’ PROPN iajs-3911 162 76 [ [ PUNCT iajs-3911 162 77 βˆ’1 βˆ’1 NOUN iajs-3911 162 78 𝑛 𝑛 PROPN iajs-3911 162 79 ( ( PUNCT iajs-3911 162 80 1 1 NUM iajs-3911 162 81 𝛼2 𝛼2 ADJ iajs-3911 162 82 + + CCONJ iajs-3911 162 83 βˆ‘ βˆ‘ PROPN iajs-3911 162 84 1 1 NUM iajs-3911 162 85 ( ( PUNCT iajs-3911 162 86 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 162 87 ) ) PUNCT iajs-3911 162 88 2 2 NUM iajs-3911 162 89 𝑛 𝑛 PROPN iajs-3911 162 90 𝑖=1 𝑖=1 PROPN iajs-3911 162 91 ) ) PUNCT iajs-3911 162 92 ] ] PUNCT iajs-3911 162 93 βˆ’1 βˆ’1 NOUN iajs-3911 163 1 = = SYM iajs-3911 163 2 𝑛 𝑛 PRON iajs-3911 163 3 1 1 NUM iajs-3911 164 1 𝛼2+βˆ‘ 𝛼2+βˆ‘ PROPN iajs-3911 164 2 1 1 NUM iajs-3911 164 3 ( ( PUNCT iajs-3911 164 4 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 164 5 ) ) PUNCT iajs-3911 164 6 2 2 NUM iajs-3911 164 7 𝑛 𝑛 PRON iajs-3911 164 8 𝑖=1 𝑖=1 PROPN iajs-3911 164 9 ( ( PUNCT iajs-3911 164 10 35 35 NUM iajs-3911 164 11 ) ) PUNCT iajs-3911 164 12 οΏ½ οΏ½ PROPN iajs-3911 164 13 Μ‚ Μ‚ SYM iajs-3911 164 14 οΏ½ οΏ½ NOUN iajs-3911 164 15 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 NOUN iajs-3911 164 16 = = PUNCT iajs-3911 164 17 [ [ PUNCT iajs-3911 164 18 |π»βˆ—| |π»βˆ—| NOUN iajs-3911 164 19 |𝐻| |𝐻| NOUN iajs-3911 164 20 ] ] SYM iajs-3911 164 21 1 1 NUM iajs-3911 164 22 2 2 NUM iajs-3911 164 23 exp exp NOUN iajs-3911 164 24 ( ( PUNCT iajs-3911 164 25 𝑛{π›΅βˆ—( 𝑛{π›΅βˆ—( NOUN iajs-3911 164 26 οΏ½ οΏ½ SYM iajs-3911 164 27 Μ‚ Μ‚ VERB iajs-3911 164 28 οΏ½ οΏ½ NOUN iajs-3911 164 29 βˆ— βˆ— NOUN iajs-3911 164 30 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NOUN iajs-3911 164 31 ) ) PUNCT iajs-3911 164 32 βˆ’ βˆ’ PROPN iajs-3911 164 33 𝑇 𝑇 PROPN iajs-3911 164 34 ( ( PUNCT iajs-3911 164 35 οΏ½ οΏ½ PROPN iajs-3911 164 36 Μ‚ Μ‚ NOUN iajs-3911 164 37 οΏ½ οΏ½ NOUN iajs-3911 164 38 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NUM iajs-3911 164 39 ) ) PUNCT iajs-3911 164 40 } } PUNCT iajs-3911 164 41 ) ) PUNCT iajs-3911 164 42 οΏ½ οΏ½ PROPN iajs-3911 164 43 Μ‚ Μ‚ SYM iajs-3911 164 44 οΏ½ οΏ½ NOUN iajs-3911 164 45 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 NOUN iajs-3911 164 46 = = PUNCT iajs-3911 164 47 [ [ PUNCT iajs-3911 164 48 𝑛 𝑛 PROPN iajs-3911 164 49 1 1 NUM iajs-3911 164 50 𝛼2+βˆ‘ 𝛼2+βˆ‘ PROPN iajs-3911 164 51 1 1 NUM iajs-3911 164 52 ( ( PUNCT iajs-3911 164 53 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 164 54 ) ) PUNCT iajs-3911 164 55 2 2 NUM iajs-3911 164 56 𝑛 𝑛 NOUN iajs-3911 164 57 𝑖=1 𝑖=1 PUNCT iajs-3911 164 58 𝑛 𝑛 PRON iajs-3911 164 59 βˆ‘ βˆ‘ ADP iajs-3911 164 60 1 1 NUM iajs-3911 164 61 ( ( PUNCT iajs-3911 164 62 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 164 63 ) ) PUNCT iajs-3911 164 64 2 2 NUM iajs-3911 164 65 𝑛 𝑛 PRON iajs-3911 164 66 𝑖=1 𝑖=1 PUNCT iajs-3911 164 67 ] ] PUNCT iajs-3911 164 68 1 1 NUM iajs-3911 164 69 2 2 NUM iajs-3911 164 70 exp exp NOUN iajs-3911 164 71 ( ( PUNCT iajs-3911 164 72 𝑛 𝑛 PROPN iajs-3911 164 73 { { PUNCT iajs-3911 164 74 ln(𝛼 ln(𝛼 NOUN iajs-3911 164 75 ) ) PUNCT iajs-3911 164 76 𝑛 𝑛 PROPN iajs-3911 164 77 + + ADJ iajs-3911 164 78 βˆ‘ βˆ‘ PROPN iajs-3911 164 79 ln(𝛼+πœ†π‘‘π‘– ln(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 164 80 ) ) PUNCT iajs-3911 164 81 𝑛 𝑛 PROPN iajs-3911 164 82 𝑖=1 𝑖=1 PUNCT iajs-3911 164 83 𝑛 𝑛 PRON iajs-3911 164 84 βˆ’ βˆ’ NOUN iajs-3911 164 85 𝛼 𝛼 INTJ iajs-3911 164 86 βˆ‘ βˆ‘ PROPN iajs-3911 164 87 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 164 88 𝑛 𝑛 PROPN iajs-3911 164 89 𝑖=1 𝑖=1 PUNCT iajs-3911 164 90 𝑛 𝑛 PRON iajs-3911 164 91 βˆ’ βˆ’ PROPN iajs-3911 164 92 πœƒπ›Ό πœƒπ›Ό VERB iajs-3911 164 93 𝑛 𝑛 PROPN iajs-3911 164 94 ( ( PUNCT iajs-3911 164 95 1 1 NUM iajs-3911 164 96 𝛼 𝛼 NOUN iajs-3911 164 97 + + NOUN iajs-3911 164 98 βˆ‘ βˆ‘ PROPN iajs-3911 164 99 1 1 NUM iajs-3911 164 100 ( ( PUNCT iajs-3911 164 101 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 164 102 ) ) PUNCT iajs-3911 164 103 𝑛 𝑛 PRON iajs-3911 164 104 𝑖=1 𝑖=1 PUNCT iajs-3911 164 105 βˆ‘ βˆ‘ PROPN iajs-3911 164 106 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 164 107 𝑛 𝑛 PROPN iajs-3911 164 108 𝑖=1 𝑖=1 PROPN iajs-3911 164 109 βˆ’ βˆ’ NUM iajs-3911 164 110 πœƒ πœƒ NOUN iajs-3911 164 111 ) ) PUNCT iajs-3911 164 112 βˆ’ βˆ’ PROPN iajs-3911 165 1 ( ( PUNCT iajs-3911 165 2 βˆ‘ βˆ‘ INTJ iajs-3911 165 3 ln(𝛼+πœ†π‘‘π‘– ln(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 165 4 ) ) PUNCT iajs-3911 165 5 𝑛 𝑛 PROPN iajs-3911 165 6 𝑖=1 𝑖=1 PUNCT iajs-3911 166 1 𝑛 𝑛 DET iajs-3911 166 2 βˆ’ βˆ’ NOUN iajs-3911 166 3 𝛼 𝛼 INTJ iajs-3911 166 4 βˆ‘ βˆ‘ PROPN iajs-3911 166 5 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 166 6 𝑛 𝑛 PROPN iajs-3911 166 7 𝑖=1 𝑖=1 PUNCT iajs-3911 166 8 𝑛 𝑛 PRON iajs-3911 166 9 βˆ’ βˆ’ PROPN iajs-3911 166 10 πœƒπ›Ό πœƒπ›Ό VERB iajs-3911 166 11 𝑛 𝑛 PROPN iajs-3911 166 12 ( ( PUNCT iajs-3911 166 13 βˆ‘ βˆ‘ PROPN iajs-3911 166 14 1 1 NUM iajs-3911 166 15 ( ( PUNCT iajs-3911 166 16 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 166 17 ) ) PUNCT iajs-3911 166 18 𝑛 𝑛 PRON iajs-3911 166 19 𝑖=1 𝑖=1 PUNCT iajs-3911 166 20 βˆ’ βˆ’ PROPN iajs-3911 166 21 βˆ‘ βˆ‘ PROPN iajs-3911 166 22 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 166 23 𝑛 𝑛 PROPN iajs-3911 166 24 𝑖=1 𝑖=1 PROPN iajs-3911 166 25 βˆ’ βˆ’ NUM iajs-3911 166 26 πœƒ πœƒ NOUN iajs-3911 166 27 ) ) PUNCT iajs-3911 166 28 ) ) PUNCT iajs-3911 166 29 } } PUNCT iajs-3911 166 30 ) ) PUNCT iajs-3911 166 31 ( ( PUNCT iajs-3911 166 32 36 36 NUM iajs-3911 166 33 ) ) PUNCT iajs-3911 166 34 οΏ½ οΏ½ PROPN iajs-3911 166 35 Μ‚ Μ‚ SYM iajs-3911 166 36 οΏ½ οΏ½ NOUN iajs-3911 166 37 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 NOUN iajs-3911 166 38 = = PUNCT iajs-3911 167 1 [ [ PUNCT iajs-3911 167 2 βˆ‘ βˆ‘ PROPN iajs-3911 167 3 1 1 NUM iajs-3911 167 4 ( ( PUNCT iajs-3911 167 5 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 167 6 ) ) PUNCT iajs-3911 167 7 2 2 NUM iajs-3911 167 8 𝑛 𝑛 PRON iajs-3911 167 9 𝑖=1 𝑖=1 PROPN iajs-3911 167 10 1 1 NUM iajs-3911 167 11 𝛼2+βˆ‘ 𝛼2+βˆ‘ PROPN iajs-3911 167 12 1 1 NUM iajs-3911 167 13 ( ( PUNCT iajs-3911 167 14 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 167 15 ) ) PUNCT iajs-3911 167 16 2 2 NUM iajs-3911 167 17 𝑛 𝑛 PRON iajs-3911 167 18 𝑖=1 𝑖=1 PUNCT iajs-3911 167 19 ] ] PUNCT iajs-3911 167 20 1 1 NUM iajs-3911 167 21 2 2 NUM iajs-3911 167 22 ( ( PUNCT iajs-3911 167 23 1 1 NUM iajs-3911 167 24 + + NUM iajs-3911 167 25 𝛼 𝛼 X iajs-3911 167 26 βˆ‘ βˆ‘ PROPN iajs-3911 167 27 1 1 NUM iajs-3911 167 28 ( ( PUNCT iajs-3911 167 29 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 167 30 ) ) PUNCT iajs-3911 167 31 𝑛 𝑛 PRON iajs-3911 167 32 𝑖=1 𝑖=1 PUNCT iajs-3911 167 33 βˆ’ βˆ’ PUNCT iajs-3911 167 34 𝛼 𝛼 X iajs-3911 167 35 βˆ‘ βˆ‘ PUNCT iajs-3911 167 36 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 167 37 𝑛 𝑛 PRON iajs-3911 167 38 𝑖=1 𝑖=1 PROPN iajs-3911 167 39 βˆ’ βˆ’ PROPN iajs-3911 167 40 π›Όπœƒ)𝑒π‘₯𝑝 π›Όπœƒ)𝑒π‘₯𝑝 NOUN iajs-3911 167 41 ( ( PUNCT iajs-3911 167 42 βˆ‘ βˆ‘ PUNCT iajs-3911 167 43 𝑙𝑛(𝛼+πœ†π‘‘π‘– 𝑙𝑛(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 167 44 ) ) PUNCT iajs-3911 167 45 𝑛 𝑛 PRON iajs-3911 167 46 𝑖=1 𝑖=1 PROPN iajs-3911 167 47 𝛼 𝛼 NUM iajs-3911 167 48 βˆ’ βˆ’ PROPN iajs-3911 167 49 βˆ‘ βˆ‘ PROPN iajs-3911 167 50 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 167 51 𝑛 𝑛 PROPN iajs-3911 167 52 𝑖=1 𝑖=1 PROPN iajs-3911 167 53 βˆ’ βˆ’ PROPN iajs-3911 167 54 πœƒ πœƒ NOUN iajs-3911 167 55 ) ) PUNCT iajs-3911 167 56 ( ( PUNCT iajs-3911 167 57 37 37 NUM iajs-3911 167 58 ) ) PUNCT iajs-3911 167 59 ihjpas ihjpa NOUN iajs-3911 167 60 . . PUNCT iajs-3911 168 1 2025,38(2 2025,38(2 PROPN iajs-3911 168 2 ) ) PUNCT iajs-3911 168 3 409 409 NUM iajs-3911 168 4 estimation estimation NOUN iajs-3911 168 5 of of ADP iajs-3911 168 6 parameter parameter NOUN iajs-3911 168 7 πœ† πœ† ADP iajs-3911 168 8 when when SCONJ iajs-3911 168 9 the the DET iajs-3911 168 10 parameter parameter NOUN iajs-3911 168 11 𝛼 𝛼 NOUN iajs-3911 168 12 is be AUX iajs-3911 168 13 knows know VERB iajs-3911 168 14 . . PUNCT iajs-3911 169 1 assume assume VERB iajs-3911 169 2 that that SCONJ iajs-3911 169 3 πœ™(𝛼 πœ™(𝛼 NOUN iajs-3911 169 4 , , PUNCT iajs-3911 169 5 πœ† πœ† NOUN iajs-3911 169 6 ) ) PUNCT iajs-3911 169 7 = = SYM iajs-3911 169 8 πœ† πœ† NOUN iajs-3911 169 9 in in ADP iajs-3911 169 10 equation equation NOUN iajs-3911 169 11 ( ( PUNCT iajs-3911 169 12 27 27 NUM iajs-3911 169 13 ) ) PUNCT iajs-3911 169 14 and and CCONJ iajs-3911 169 15 then then ADV iajs-3911 169 16 οΏ½ οΏ½ PROPN iajs-3911 169 17 Μ‚ Μ‚ SYM iajs-3911 169 18 οΏ½ οΏ½ NOUN iajs-3911 169 19 = = SYM iajs-3911 169 20 𝐸(πœ†|𝑑 𝐸(πœ†|𝑑 NOUN iajs-3911 169 21 ) ) PUNCT iajs-3911 169 22 , , PUNCT iajs-3911 169 23 where where SCONJ iajs-3911 169 24 οΏ½ οΏ½ PROPN iajs-3911 169 25 Μ‚ Μ‚ SYM iajs-3911 169 26 οΏ½ οΏ½ PROPN iajs-3911 169 27 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 PROPN iajs-3911 169 28 denote denote VERB iajs-3911 169 29 the the DET iajs-3911 169 30 bayes bayes PROPN iajs-3911 169 31 estimator estimator NOUN iajs-3911 169 32 of of ADP iajs-3911 169 33 πœ† πœ† ADP iajs-3911 169 34 according accord VERB iajs-3911 169 35 to to ADP iajs-3911 169 36 tierney tierney PROPN iajs-3911 169 37 and and CCONJ iajs-3911 169 38 kadane kadane PROPN iajs-3911 169 39 approximation approximation NOUN iajs-3911 169 40 method method NOUN iajs-3911 169 41 . . PUNCT iajs-3911 170 1 οΏ½ οΏ½ PROPN iajs-3911 170 2 Μ‚ Μ‚ VERB iajs-3911 170 3 οΏ½ οΏ½ PROPN iajs-3911 170 4 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 PROPN iajs-3911 170 5 = = PROPN iajs-3911 170 6 πœƒ πœƒ PROPN iajs-3911 170 7 π‘’βˆ’π›Ό π‘’βˆ’π›Ό PROPN iajs-3911 170 8 βˆ‘ βˆ‘ PUNCT iajs-3911 170 9 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 170 10 𝑛 𝑛 PROPN iajs-3911 170 11 𝑖=1 𝑖=1 PROPN iajs-3911 170 12 ∫ ∫ PROPN iajs-3911 170 13 πœ† πœ† PROPN iajs-3911 170 14 ∏ ∏ PROPN iajs-3911 170 15 ( ( PUNCT iajs-3911 170 16 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 170 17 ) ) PUNCT iajs-3911 170 18 𝑛 𝑛 PROPN iajs-3911 170 19 𝑖=1 𝑖=1 PROPN iajs-3911 170 20 𝑒 𝑒 PROPN iajs-3911 170 21 βˆ’πœ† βˆ’πœ† PROPN iajs-3911 170 22 ( ( PUNCT iajs-3911 170 23 βˆ‘ βˆ‘ PROPN iajs-3911 170 24 𝑑𝑖 𝑑𝑖 PRON iajs-3911 170 25 2𝑛 2𝑛 PROPN iajs-3911 170 26 𝑖=1 𝑖=1 PROPN iajs-3911 170 27 2 2 NUM iajs-3911 170 28 + + NOUN iajs-3911 170 29 πœƒ πœƒ NOUN iajs-3911 170 30 ) ) PUNCT iajs-3911 170 31 π‘‘πœ† π‘‘πœ† ADP iajs-3911 170 32 ∞ ∞ PROPN iajs-3911 170 33 0 0 NUM iajs-3911 170 34 πœƒπ‘’βˆ’π›Όβˆ‘ πœƒπ‘’βˆ’π›Όβˆ‘ X iajs-3911 170 35 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 170 36 𝑛 𝑛 PROPN iajs-3911 170 37 𝑖=1 𝑖=1 PROPN iajs-3911 170 38 ∫ ∫ PROPN iajs-3911 170 39 ∏ ∏ PROPN iajs-3911 170 40 ( ( PUNCT iajs-3911 170 41 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 170 42 ) ) PUNCT iajs-3911 170 43 𝑛 𝑛 PROPN iajs-3911 170 44 𝑖=1 𝑖=1 PROPN iajs-3911 170 45 𝑒 𝑒 PROPN iajs-3911 170 46 βˆ’πœ† βˆ’πœ† PROPN iajs-3911 170 47 ( ( PUNCT iajs-3911 170 48 βˆ‘ βˆ‘ PROPN iajs-3911 170 49 𝑑𝑖 𝑑𝑖 PRON iajs-3911 170 50 2𝑛 2𝑛 PROPN iajs-3911 170 51 𝑖=1 𝑖=1 PROPN iajs-3911 170 52 2 2 NUM iajs-3911 170 53 + + NOUN iajs-3911 170 54 πœƒ πœƒ NOUN iajs-3911 170 55 ) ) PUNCT iajs-3911 170 56 π‘‘πœ† π‘‘πœ† ADP iajs-3911 170 57 ∞ ∞ PROPN iajs-3911 170 58 0 0 NUM iajs-3911 170 59 ( ( PUNCT iajs-3911 170 60 38 38 NUM iajs-3911 170 61 ) ) PUNCT iajs-3911 170 62 and and CCONJ iajs-3911 170 63 Ο„ Ο„ PROPN iajs-3911 170 64 = = NOUN iajs-3911 170 65 𝑙𝑛 𝑙𝑛 X iajs-3911 170 66 𝑛 𝑛 PROPN iajs-3911 171 1 [ [ X iajs-3911 171 2 ∏ ∏ X iajs-3911 171 3 ( ( PUNCT iajs-3911 171 4 𝛼 𝛼 NOUN iajs-3911 171 5 + + NUM iajs-3911 171 6 πœ†π‘‘π‘– πœ†π‘‘π‘– NOUN iajs-3911 171 7 ) ) PUNCT iajs-3911 171 8 𝑒 𝑒 PROPN iajs-3911 171 9 βˆ’πœ† βˆ’πœ† PROPN iajs-3911 171 10 ( ( PUNCT iajs-3911 171 11 βˆ‘ βˆ‘ PROPN iajs-3911 171 12 𝑑𝑖 𝑑𝑖 PRON iajs-3911 171 13 2𝑛 2𝑛 PROPN iajs-3911 171 14 𝑖=1 𝑖=1 PROPN iajs-3911 171 15 2 2 NUM iajs-3911 171 16 + + NOUN iajs-3911 171 17 πœƒ πœƒ NOUN iajs-3911 171 18 ) ) PUNCT iajs-3911 171 19 𝑛 𝑛 PRON iajs-3911 171 20 𝑖=1 𝑖=1 PUNCT iajs-3911 171 21 ] ] PUNCT iajs-3911 171 22 = = PUNCT iajs-3911 171 23 βˆ‘ βˆ‘ PUNCT iajs-3911 171 24 ln(𝛼+πœ†π‘‘π‘– ln(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 171 25 ) ) PUNCT iajs-3911 171 26 𝑛 𝑛 PROPN iajs-3911 171 27 𝑖=1 𝑖=1 PUNCT iajs-3911 172 1 𝑛 𝑛 DET iajs-3911 172 2 βˆ’ βˆ’ NOUN iajs-3911 172 3 πœ† πœ† X iajs-3911 172 4 ( ( PUNCT iajs-3911 172 5 βˆ‘ βˆ‘ PROPN iajs-3911 172 6 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 172 7 2𝑛 2𝑛 PROPN iajs-3911 172 8 𝑖=1 𝑖=1 PROPN iajs-3911 172 9 2 2 NUM iajs-3911 172 10 + + NOUN iajs-3911 172 11 πœƒ πœƒ NOUN iajs-3911 172 12 ) ) PUNCT iajs-3911 172 13 𝑛 𝑛 PROPN iajs-3911 172 14 ( ( PUNCT iajs-3911 172 15 39 39 NUM iajs-3911 172 16 ) ) PUNCT iajs-3911 172 17 Ο„βˆ— Ο„βˆ— NOUN iajs-3911 172 18 = = PUNCT iajs-3911 172 19 𝑙𝑛 𝑙𝑛 NOUN iajs-3911 172 20 𝑛 𝑛 PROPN iajs-3911 173 1 [ [ X iajs-3911 173 2 πœ† πœ† X iajs-3911 173 3 ∏ ∏ PROPN iajs-3911 173 4 ( ( PUNCT iajs-3911 173 5 𝛼 𝛼 NOUN iajs-3911 173 6 + + NUM iajs-3911 173 7 πœ†π‘‘π‘– πœ†π‘‘π‘– NOUN iajs-3911 173 8 ) ) PUNCT iajs-3911 173 9 𝑛 𝑛 PROPN iajs-3911 173 10 𝑖=1 𝑖=1 PROPN iajs-3911 173 11 𝑒 𝑒 PROPN iajs-3911 173 12 βˆ’πœ† βˆ’πœ† PROPN iajs-3911 173 13 ( ( PUNCT iajs-3911 173 14 βˆ‘ βˆ‘ PROPN iajs-3911 173 15 𝑑𝑖 𝑑𝑖 PRON iajs-3911 173 16 2𝑛 2𝑛 PROPN iajs-3911 173 17 𝑖=1 𝑖=1 PROPN iajs-3911 173 18 2 2 NUM iajs-3911 173 19 + + NOUN iajs-3911 173 20 πœƒ πœƒ NOUN iajs-3911 173 21 ) ) PUNCT iajs-3911 173 22 ] ] PUNCT iajs-3911 174 1 = = PUNCT iajs-3911 174 2 ln(πœ† ln(πœ† X iajs-3911 174 3 ) ) PUNCT iajs-3911 175 1 𝑛 𝑛 PROPN iajs-3911 176 1 + + ADJ iajs-3911 176 2 βˆ‘ βˆ‘ PROPN iajs-3911 176 3 ln(𝛼+πœ†π‘‘π‘– ln(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 176 4 ) ) PUNCT iajs-3911 176 5 𝑛 𝑛 PROPN iajs-3911 176 6 𝑖=1 𝑖=1 PUNCT iajs-3911 177 1 𝑛 𝑛 DET iajs-3911 177 2 βˆ’ βˆ’ NOUN iajs-3911 177 3 πœ† πœ† X iajs-3911 177 4 ( ( PUNCT iajs-3911 177 5 βˆ‘ βˆ‘ PROPN iajs-3911 177 6 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 177 7 2𝑛 2𝑛 PROPN iajs-3911 177 8 𝑖=1 𝑖=1 PROPN iajs-3911 177 9 2 2 NUM iajs-3911 177 10 + + NOUN iajs-3911 177 11 πœƒ πœƒ NOUN iajs-3911 177 12 ) ) PUNCT iajs-3911 177 13 𝑛 𝑛 PROPN iajs-3911 177 14 ( ( PUNCT iajs-3911 177 15 40 40 NUM iajs-3911 177 16 ) ) PUNCT iajs-3911 177 17 to to PART iajs-3911 177 18 find find VERB iajs-3911 177 19 πœ†π‘šπ‘Žπ‘₯ πœ†π‘šπ‘Žπ‘₯ PRON iajs-3911 177 20 and and CCONJ iajs-3911 177 21 πœ†βˆ— πœ†βˆ— NOUN iajs-3911 177 22 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ PRON iajs-3911 177 23 which which PRON iajs-3911 177 24 are be AUX iajs-3911 177 25 the the DET iajs-3911 177 26 values value NOUN iajs-3911 177 27 that that PRON iajs-3911 177 28 maximize maximize VERB iajs-3911 177 29 Ο„ Ο„ PROPN iajs-3911 177 30 and and CCONJ iajs-3911 177 31 Ο„βˆ—respectively Ο„βˆ—respectively ADV iajs-3911 177 32 : : PUNCT iajs-3911 177 33 πœ•Ο„ πœ•Ο„ ADJ iajs-3911 177 34 πœ•πœ† πœ•πœ† NOUN iajs-3911 177 35 = = PUNCT iajs-3911 177 36 βˆ‘ βˆ‘ PROPN iajs-3911 177 37 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 177 38 ( ( PUNCT iajs-3911 177 39 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 177 40 ) ) PUNCT iajs-3911 178 1 𝑛 𝑛 PROPN iajs-3911 178 2 𝑖=1 𝑖=1 PUNCT iajs-3911 179 1 𝑛 𝑛 DET iajs-3911 179 2 βˆ’ βˆ’ PROPN iajs-3911 179 3 ( ( PUNCT iajs-3911 179 4 βˆ‘ βˆ‘ PROPN iajs-3911 179 5 𝑑𝑖 𝑑𝑖 PRON iajs-3911 179 6 2𝑛 2𝑛 PROPN iajs-3911 179 7 𝑖=1 𝑖=1 PROPN iajs-3911 179 8 2 2 NUM iajs-3911 179 9 + + NOUN iajs-3911 179 10 πœƒ πœƒ NOUN iajs-3911 179 11 ) ) PUNCT iajs-3911 179 12 𝑛 𝑛 PRON iajs-3911 179 13 πœ•Ο„βˆ— πœ•Ο„βˆ— PROPN iajs-3911 179 14 πœ•πœ† πœ•πœ† NOUN iajs-3911 179 15 = = NOUN iajs-3911 179 16 1 1 NUM iajs-3911 179 17 π‘›πœ† π‘›πœ† NOUN iajs-3911 179 18 + + CCONJ iajs-3911 179 19 βˆ‘ βˆ‘ PROPN iajs-3911 179 20 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 179 21 ( ( PUNCT iajs-3911 179 22 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 179 23 ) ) PUNCT iajs-3911 179 24 𝑛 𝑛 PROPN iajs-3911 179 25 𝑖=1 𝑖=1 PUNCT iajs-3911 179 26 𝑛 𝑛 PRON iajs-3911 179 27 βˆ’ βˆ’ PROPN iajs-3911 180 1 ( ( PUNCT iajs-3911 180 2 βˆ‘ βˆ‘ PROPN iajs-3911 180 3 𝑑𝑖 𝑑𝑖 PRON iajs-3911 180 4 2𝑛 2𝑛 PROPN iajs-3911 180 5 𝑖=1 𝑖=1 PROPN iajs-3911 180 6 2 2 NUM iajs-3911 180 7 + + NOUN iajs-3911 180 8 πœƒ πœƒ NOUN iajs-3911 180 9 ) ) PUNCT iajs-3911 180 10 𝑛 𝑛 PRON iajs-3911 180 11 οΏ½ οΏ½ PROPN iajs-3911 180 12 Μ‚ Μ‚ NOUN iajs-3911 180 13 οΏ½ οΏ½ NOUN iajs-3911 180 14 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NOUN iajs-3911 180 15 = = PUNCT iajs-3911 180 16 βˆ‘ βˆ‘ PROPN iajs-3911 180 17 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 180 18 ( ( PUNCT iajs-3911 180 19 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 180 20 ) ) PUNCT iajs-3911 180 21 𝑛 𝑛 PRON iajs-3911 180 22 𝑖=1 𝑖=1 PUNCT iajs-3911 181 1 βˆ’ βˆ’ PROPN iajs-3911 181 2 ( ( PUNCT iajs-3911 181 3 βˆ‘ βˆ‘ PROPN iajs-3911 181 4 𝑑𝑖 𝑑𝑖 PRON iajs-3911 181 5 2𝑛 2𝑛 PROPN iajs-3911 181 6 𝑖=1 𝑖=1 PROPN iajs-3911 181 7 2 2 NUM iajs-3911 181 8 + + NUM iajs-3911 181 9 πœƒ πœƒ X iajs-3911 181 10 ) ) PUNCT iajs-3911 181 11 οΏ½ οΏ½ PROPN iajs-3911 181 12 Μ‚ Μ‚ VERB iajs-3911 181 13 οΏ½ οΏ½ NOUN iajs-3911 181 14 βˆ— βˆ— NOUN iajs-3911 181 15 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NOUN iajs-3911 181 16 = = NOUN iajs-3911 181 17 1 1 NUM iajs-3911 181 18 πœ† πœ† NOUN iajs-3911 181 19 + + PROPN iajs-3911 181 20 βˆ‘ βˆ‘ PROPN iajs-3911 181 21 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 181 22 ( ( PUNCT iajs-3911 181 23 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 181 24 ) ) PUNCT iajs-3911 181 25 βˆ’ βˆ’ PROPN iajs-3911 181 26 ( ( PUNCT iajs-3911 181 27 βˆ‘ βˆ‘ PROPN iajs-3911 181 28 𝑑𝑖 𝑑𝑖 PRON iajs-3911 181 29 2𝑛 2𝑛 PROPN iajs-3911 181 30 𝑖=1 𝑖=1 PROPN iajs-3911 181 31 2 2 NUM iajs-3911 181 32 + + CCONJ iajs-3911 181 33 πœƒ)𝑛 πœƒ)𝑛 X iajs-3911 181 34 𝑖=1 𝑖=1 PROPN iajs-3911 181 35 οΏ½ οΏ½ PROPN iajs-3911 181 36 Μ‚ Μ‚ VERB iajs-3911 181 37 οΏ½ οΏ½ NOUN iajs-3911 181 38 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ VERB iajs-3911 181 39 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-3911 181 40 οΏ½ οΏ½ PROPN iajs-3911 181 41 Μ‚ Μ‚ NOUN iajs-3911 181 42 οΏ½ οΏ½ NOUN iajs-3911 181 43 βˆ— βˆ— NOUN iajs-3911 181 44 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NOUN iajs-3911 181 45 is be AUX iajs-3911 181 46 maximum maximum ADJ iajs-3911 181 47 since since SCONJ iajs-3911 181 48 : : PUNCT iajs-3911 181 49 πœ•2Ο„βˆ— πœ•2Ο„βˆ— PROPN iajs-3911 181 50 πœ•2πœ† πœ•2πœ† X iajs-3911 181 51 = = SYM iajs-3911 181 52 βˆ’1 βˆ’1 NOUN iajs-3911 181 53 𝑛 𝑛 PROPN iajs-3911 181 54 ( ( PUNCT iajs-3911 181 55 1 1 NUM iajs-3911 181 56 πœ†2 πœ†2 NOUN iajs-3911 182 1 + + CCONJ iajs-3911 182 2 βˆ‘ βˆ‘ PROPN iajs-3911 182 3 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 182 4 2 2 NUM iajs-3911 182 5 ( ( PUNCT iajs-3911 182 6 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 182 7 ) ) PUNCT iajs-3911 182 8 2 2 NUM iajs-3911 182 9 𝑛 𝑛 PRON iajs-3911 182 10 𝑖=1 𝑖=1 PUNCT iajs-3911 182 11 ) ) PUNCT iajs-3911 182 12 < < X iajs-3911 182 13 0 0 PUNCT iajs-3911 182 14 and and CCONJ iajs-3911 182 15 πœ•2Ο„ πœ•2Ο„ NUM iajs-3911 182 16 πœ•2πœ† πœ•2πœ† VERB iajs-3911 182 17 = = SYM iajs-3911 182 18 βˆ’1 βˆ’1 NOUN iajs-3911 182 19 𝑛 𝑛 PROPN iajs-3911 182 20 βˆ‘ βˆ‘ ADP iajs-3911 182 21 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 182 22 2 2 NUM iajs-3911 182 23 ( ( PUNCT iajs-3911 182 24 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 182 25 ) ) PUNCT iajs-3911 182 26 2 2 NUM iajs-3911 182 27 𝑛 𝑛 PRON iajs-3911 182 28 𝑖=1 𝑖=1 PUNCT iajs-3911 182 29 < < X iajs-3911 182 30 0 0 NUM iajs-3911 182 31 necessary necessary ADJ iajs-3911 182 32 and and CCONJ iajs-3911 182 33 sufficient sufficient ADJ iajs-3911 182 34 is be AUX iajs-3911 182 35 that that DET iajs-3911 182 36 second second ADJ iajs-3911 182 37 derivate derivate NOUN iajs-3911 182 38 respect respect NOUN iajs-3911 182 39 to to ADP iajs-3911 182 40 πœ† πœ† NOUN iajs-3911 182 41 is be AUX iajs-3911 182 42 negative negative ADJ iajs-3911 182 43 . . PUNCT iajs-3911 183 1 the the DET iajs-3911 183 2 determinant determinant NOUN iajs-3911 183 3 of of ADP iajs-3911 183 4 the the DET iajs-3911 183 5 negative negative NOUN iajs-3911 183 6 of of ADP iajs-3911 183 7 the the DET iajs-3911 183 8 inverse inverse NOUN iajs-3911 183 9 hessian hessian NOUN iajs-3911 183 10 of of ADP iajs-3911 183 11 Ο„ Ο„ PROPN iajs-3911 183 12 at at ADP iajs-3911 183 13 οΏ½ οΏ½ PROPN iajs-3911 183 14 Μ‚ Μ‚ SYM iajs-3911 183 15 οΏ½ οΏ½ NOUN iajs-3911 183 16 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ NOUN iajs-3911 183 17 and and CCONJ iajs-3911 183 18 Ο„βˆ— Ο„βˆ— NOUN iajs-3911 183 19 at at ADP iajs-3911 183 20 οΏ½ οΏ½ PROPN iajs-3911 183 21 Μ‚ Μ‚ NOUN iajs-3911 183 22 οΏ½ οΏ½ NOUN iajs-3911 183 23 βˆ— βˆ— NOUN iajs-3911 183 24 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ PRON iajs-3911 183 25 respectively respectively ADV iajs-3911 183 26 : : PUNCT iajs-3911 183 27 𝐻 𝐻 PROPN iajs-3911 183 28 = = SYM iajs-3911 183 29 βˆ’ βˆ’ PROPN iajs-3911 183 30 [ [ PUNCT iajs-3911 183 31 πœ•2Ο„ πœ•2Ο„ NOUN iajs-3911 183 32 πœ•2πœ† πœ•2πœ† PRON iajs-3911 183 33 ] ] PUNCT iajs-3911 183 34 βˆ’1 βˆ’1 NOUN iajs-3911 183 35 πœ†=πœ†π‘šπ‘Žπ‘₯ πœ†=πœ†π‘šπ‘Žπ‘₯ NOUN iajs-3911 184 1 = = SYM iajs-3911 184 2 βˆ’ βˆ’ PROPN iajs-3911 184 3 [ [ PUNCT iajs-3911 184 4 βˆ’1 βˆ’1 NOUN iajs-3911 184 5 𝑛 𝑛 ADP iajs-3911 184 6 βˆ‘ βˆ‘ ADP iajs-3911 184 7 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 184 8 2 2 NUM iajs-3911 184 9 ( ( PUNCT iajs-3911 184 10 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 184 11 ) ) PUNCT iajs-3911 184 12 2 2 NUM iajs-3911 184 13 𝑛 𝑛 PRON iajs-3911 184 14 𝑖=1 𝑖=1 PROPN iajs-3911 184 15 ] ] PUNCT iajs-3911 184 16 βˆ’1 βˆ’1 NOUN iajs-3911 185 1 = = SYM iajs-3911 185 2 𝑛 𝑛 PRON iajs-3911 185 3 βˆ‘ βˆ‘ ADP iajs-3911 185 4 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 185 5 2 2 NUM iajs-3911 185 6 ( ( PUNCT iajs-3911 185 7 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 185 8 ) ) PUNCT iajs-3911 185 9 2 2 NUM iajs-3911 185 10 𝑛 𝑛 PRON iajs-3911 185 11 𝑖=1 𝑖=1 PROPN iajs-3911 185 12 ( ( PUNCT iajs-3911 185 13 41 41 NUM iajs-3911 185 14 ) ) PUNCT iajs-3911 185 15 οΏ½ οΏ½ PROPN iajs-3911 185 16 Μ‚ Μ‚ SYM iajs-3911 185 17 οΏ½ οΏ½ NOUN iajs-3911 185 18 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 NOUN iajs-3911 185 19 = = PUNCT iajs-3911 185 20 [ [ PUNCT iajs-3911 185 21 𝑛 𝑛 PROPN iajs-3911 185 22 1 1 NUM iajs-3911 185 23 πœ†2+βˆ‘ πœ†2+βˆ‘ NOUN iajs-3911 185 24 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 185 25 2 2 NUM iajs-3911 185 26 ( ( PUNCT iajs-3911 185 27 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 185 28 ) ) PUNCT iajs-3911 185 29 2 2 NUM iajs-3911 185 30 𝑛 𝑛 NOUN iajs-3911 185 31 𝑖=1 𝑖=1 PUNCT iajs-3911 185 32 𝑛 𝑛 PRON iajs-3911 185 33 βˆ‘ βˆ‘ ADP iajs-3911 185 34 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 185 35 2 2 NUM iajs-3911 185 36 ( ( PUNCT iajs-3911 185 37 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 185 38 ) ) PUNCT iajs-3911 185 39 2 2 NUM iajs-3911 185 40 𝑛 𝑛 PRON iajs-3911 185 41 𝑖=1 𝑖=1 PUNCT iajs-3911 185 42 ] ] PUNCT iajs-3911 185 43 1 1 NUM iajs-3911 185 44 2 2 NUM iajs-3911 185 45 exp exp NOUN iajs-3911 185 46 ( ( PUNCT iajs-3911 185 47 𝑛 𝑛 PROPN iajs-3911 185 48 { { PUNCT iajs-3911 185 49 ln(πœ† ln(πœ† NUM iajs-3911 185 50 ) ) PUNCT iajs-3911 185 51 𝑛 𝑛 PROPN iajs-3911 185 52 + + ADJ iajs-3911 185 53 βˆ‘ βˆ‘ PROPN iajs-3911 185 54 ln(𝛼+πœ†π‘‘π‘– ln(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 185 55 ) ) PUNCT iajs-3911 185 56 𝑛 𝑛 PROPN iajs-3911 185 57 𝑖=1 𝑖=1 PUNCT iajs-3911 186 1 𝑛 𝑛 DET iajs-3911 186 2 βˆ’ βˆ’ NOUN iajs-3911 186 3 πœ† πœ† X iajs-3911 186 4 ( ( PUNCT iajs-3911 186 5 βˆ‘ βˆ‘ PROPN iajs-3911 186 6 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 186 7 2𝑛 2𝑛 PROPN iajs-3911 186 8 𝑖=1 𝑖=1 PROPN iajs-3911 186 9 2 2 NUM iajs-3911 186 10 + + NOUN iajs-3911 186 11 πœƒ πœƒ NOUN iajs-3911 186 12 ) ) PUNCT iajs-3911 186 13 𝑛 𝑛 PROPN iajs-3911 186 14 ( ( PUNCT iajs-3911 186 15 1 1 NUM iajs-3911 186 16 πœ† πœ† X iajs-3911 186 17 + + PROPN iajs-3911 186 18 βˆ‘ βˆ‘ PROPN iajs-3911 186 19 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 186 20 ( ( PUNCT iajs-3911 186 21 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 186 22 ) ) PUNCT iajs-3911 187 1 2 2 NUM iajs-3911 187 2 𝑛 𝑛 DET iajs-3911 187 3 𝑖=1 𝑖=1 PROPN iajs-3911 187 4 βˆ’ βˆ’ PROPN iajs-3911 187 5 ( ( PUNCT iajs-3911 187 6 βˆ‘ βˆ‘ PROPN iajs-3911 187 7 𝑑𝑖 𝑑𝑖 PRON iajs-3911 187 8 2𝑛 2𝑛 PROPN iajs-3911 187 9 𝑖=1 𝑖=1 PROPN iajs-3911 187 10 2 2 NUM iajs-3911 187 11 + + NUM iajs-3911 187 12 πœƒ πœƒ NOUN iajs-3911 187 13 ) ) PUNCT iajs-3911 187 14 ) ) PUNCT iajs-3911 188 1 βˆ’ βˆ’ PROPN iajs-3911 188 2 ( ( PUNCT iajs-3911 188 3 βˆ‘ βˆ‘ INTJ iajs-3911 188 4 ln(𝛼+πœ†π‘‘π‘– ln(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 188 5 ) ) PUNCT iajs-3911 188 6 𝑛 𝑛 PROPN iajs-3911 188 7 𝑖=1 𝑖=1 PUNCT iajs-3911 189 1 𝑛 𝑛 DET iajs-3911 189 2 βˆ’ βˆ’ NOUN iajs-3911 189 3 πœ† πœ† X iajs-3911 189 4 ( ( PUNCT iajs-3911 189 5 βˆ‘ βˆ‘ PROPN iajs-3911 189 6 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 189 7 2𝑛 2𝑛 PROPN iajs-3911 189 8 𝑖=1 𝑖=1 PROPN iajs-3911 189 9 2 2 NUM iajs-3911 189 10 + + NOUN iajs-3911 189 11 πœƒ πœƒ NOUN iajs-3911 189 12 ) ) PUNCT iajs-3911 189 13 𝑛 𝑛 PROPN iajs-3911 189 14 ( ( PUNCT iajs-3911 189 15 βˆ‘ βˆ‘ PROPN iajs-3911 189 16 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 189 17 2 2 NUM iajs-3911 189 18 ( ( PUNCT iajs-3911 189 19 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 189 20 ) ) PUNCT iajs-3911 189 21 2 2 NUM iajs-3911 189 22 𝑛 𝑛 PRON iajs-3911 189 23 𝑖=1 𝑖=1 PUNCT iajs-3911 189 24 βˆ’ βˆ’ PROPN iajs-3911 190 1 ( ( PUNCT iajs-3911 190 2 βˆ‘ βˆ‘ PROPN iajs-3911 190 3 𝑑𝑖 𝑑𝑖 PRON iajs-3911 190 4 2𝑛 2𝑛 PROPN iajs-3911 190 5 𝑖=1 𝑖=1 PROPN iajs-3911 190 6 2 2 NUM iajs-3911 190 7 + + NUM iajs-3911 190 8 πœƒ πœƒ NOUN iajs-3911 190 9 ) ) PUNCT iajs-3911 190 10 ) ) PUNCT iajs-3911 190 11 ) ) PUNCT iajs-3911 190 12 } } PUNCT iajs-3911 190 13 ) ) PUNCT iajs-3911 190 14 ( ( PUNCT iajs-3911 190 15 42 42 X iajs-3911 190 16 ) ) PUNCT iajs-3911 190 17 οΏ½ οΏ½ PROPN iajs-3911 190 18 Μ‚ Μ‚ SYM iajs-3911 190 19 οΏ½ οΏ½ NOUN iajs-3911 190 20 𝐡𝑦𝑠𝑒 𝐡𝑦𝑠𝑒 NOUN iajs-3911 190 21 = = PUNCT iajs-3911 190 22 [ [ PUNCT iajs-3911 190 23 𝑛 𝑛 PROPN iajs-3911 190 24 1 1 NUM iajs-3911 190 25 πœ†2+βˆ‘ πœ†2+βˆ‘ NOUN iajs-3911 190 26 𝑑𝑖 𝑑𝑖 PROPN iajs-3911 190 27 2 2 NUM iajs-3911 190 28 ( ( PUNCT iajs-3911 190 29 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 190 30 ) ) PUNCT iajs-3911 190 31 2 2 NUM iajs-3911 190 32 𝑛 𝑛 NOUN iajs-3911 190 33 𝑖=1 𝑖=1 PUNCT iajs-3911 190 34 𝑛 𝑛 PRON iajs-3911 190 35 βˆ‘ βˆ‘ ADP iajs-3911 190 36 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 190 37 2 2 NUM iajs-3911 190 38 ( ( PUNCT iajs-3911 190 39 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 190 40 ) ) PUNCT iajs-3911 190 41 2 2 NUM iajs-3911 190 42 𝑛 𝑛 PRON iajs-3911 190 43 𝑖=1 𝑖=1 PUNCT iajs-3911 190 44 ] ] PUNCT iajs-3911 190 45 1 1 NUM iajs-3911 190 46 2 2 NUM iajs-3911 190 47 ( ( PUNCT iajs-3911 190 48 1 1 NUM iajs-3911 190 49 + + CCONJ iajs-3911 190 50 πœ† πœ† ADP iajs-3911 190 51 βˆ‘ βˆ‘ DET iajs-3911 190 52 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 190 53 ( ( PUNCT iajs-3911 190 54 𝛼+πœ†π‘‘π‘– 𝛼+πœ†π‘‘π‘– NOUN iajs-3911 190 55 ) ) PUNCT iajs-3911 190 56 𝑛 𝑛 PRON iajs-3911 190 57 𝑖=1 𝑖=1 PUNCT iajs-3911 191 1 βˆ’ βˆ’ NOUN iajs-3911 191 2 πœ† πœ† NOUN iajs-3911 191 3 ( ( PUNCT iajs-3911 191 4 βˆ‘ βˆ‘ PROPN iajs-3911 191 5 𝑑𝑖 𝑑𝑖 NOUN iajs-3911 191 6 2𝑛 2𝑛 PROPN iajs-3911 191 7 𝑖=1 𝑖=1 PROPN iajs-3911 191 8 2 2 NUM iajs-3911 191 9 + + NUM iajs-3911 191 10 πœƒ πœƒ NOUN iajs-3911 191 11 ) ) PUNCT iajs-3911 191 12 ) ) PUNCT iajs-3911 191 13 𝑒π‘₯𝑝 𝑒π‘₯𝑝 INTJ iajs-3911 191 14 ( ( PUNCT iajs-3911 191 15 βˆ‘ βˆ‘ PUNCT iajs-3911 191 16 𝑙𝑛(𝛼+πœ†π‘‘π‘– 𝑙𝑛(𝛼+πœ†π‘‘π‘– NOUN iajs-3911 191 17 ) ) PUNCT iajs-3911 191 18 𝑛 𝑛 PRON iajs-3911 191 19 𝑖=1 𝑖=1 PROPN iajs-3911 191 20 πœ† πœ† X iajs-3911 191 21 βˆ’ βˆ’ PROPN iajs-3911 191 22 ( ( PUNCT iajs-3911 191 23 βˆ‘ βˆ‘ PROPN iajs-3911 191 24 𝑑𝑖 𝑑𝑖 PRON iajs-3911 191 25 2𝑛 2𝑛 PROPN iajs-3911 191 26 𝑖=1 𝑖=1 PROPN iajs-3911 191 27 2 2 NUM iajs-3911 191 28 + + NUM iajs-3911 191 29 πœƒ πœƒ NOUN iajs-3911 191 30 ) ) PUNCT iajs-3911 191 31 ) ) PUNCT iajs-3911 191 32 ( ( PUNCT iajs-3911 191 33 43 43 X iajs-3911 191 34 ) ) PUNCT iajs-3911 191 35 ihjpas ihjpa NOUN iajs-3911 191 36 . . PUNCT iajs-3911 192 1 2025,38(2 2025,38(2 PROPN iajs-3911 192 2 ) ) PUNCT iajs-3911 192 3 410 410 NUM iajs-3911 192 4 3 3 NUM iajs-3911 192 5 . . PUNCT iajs-3911 192 6 simulation simulation NOUN iajs-3911 192 7 technique technique NOUN iajs-3911 192 8 the the DET iajs-3911 192 9 simulation simulation NOUN iajs-3911 192 10 procedure procedure NOUN iajs-3911 192 11 is be AUX iajs-3911 192 12 now now ADV iajs-3911 192 13 generally generally ADV iajs-3911 192 14 used use VERB iajs-3911 192 15 in in ADP iajs-3911 192 16 many many ADJ iajs-3911 192 17 branches branch NOUN iajs-3911 192 18 of of ADP iajs-3911 192 19 statistics statistic NOUN iajs-3911 192 20 . . PUNCT iajs-3911 193 1 they they PRON iajs-3911 193 2 can can AUX iajs-3911 193 3 be be AUX iajs-3911 193 4 used use VERB iajs-3911 193 5 to to PART iajs-3911 193 6 evaluate evaluate VERB iajs-3911 193 7 the the DET iajs-3911 193 8 behavior behavior NOUN iajs-3911 193 9 of of ADP iajs-3911 193 10 models model NOUN iajs-3911 193 11 as as ADV iajs-3911 193 12 well well ADV iajs-3911 193 13 as as ADP iajs-3911 193 14 for for ADP iajs-3911 193 15 some some DET iajs-3911 193 16 random random ADJ iajs-3911 193 17 variables variable NOUN iajs-3911 193 18 . . PUNCT iajs-3911 194 1 a a DET iajs-3911 194 2 simulation simulation NOUN iajs-3911 194 3 is be AUX iajs-3911 194 4 defined define VERB iajs-3911 194 5 as as ADP iajs-3911 194 6 a a DET iajs-3911 194 7 numerical numerical ADJ iajs-3911 194 8 scientific scientific ADJ iajs-3911 194 9 method method NOUN iajs-3911 194 10 that that PRON iajs-3911 194 11 uses use VERB iajs-3911 194 12 logical logical ADJ iajs-3911 194 13 mathematical mathematical ADJ iajs-3911 194 14 methods method NOUN iajs-3911 194 15 to to PART iajs-3911 194 16 describe describe VERB iajs-3911 194 17 the the DET iajs-3911 194 18 behavior behavior NOUN iajs-3911 194 19 of of ADP iajs-3911 194 20 a a DET iajs-3911 194 21 certain certain ADJ iajs-3911 194 22 approved approve VERB iajs-3911 194 23 system system NOUN iajs-3911 194 24 . . PUNCT iajs-3911 195 1 different different ADJ iajs-3911 195 2 techniques technique NOUN iajs-3911 195 3 have have AUX iajs-3911 195 4 been be AUX iajs-3911 195 5 conducted conduct VERB iajs-3911 195 6 . . PUNCT iajs-3911 196 1   NOUN iajs-3911 196 2 we we PRON iajs-3911 196 3 select select VERB iajs-3911 196 4 𝑛 𝑛 PRON iajs-3911 196 5 = = SYM iajs-3911 196 6 10,20,30,50 10,20,30,50 NUM iajs-3911 196 7   NOUN iajs-3911 196 8 we we PRON iajs-3911 196 9 select select VERB iajs-3911 196 10 𝛼 𝛼 VERB iajs-3911 197 1 = = SYM iajs-3911 197 2 0.25,0.5,0.75 0.25,0.5,0.75 NUM iajs-3911 197 3   NOUN iajs-3911 197 4 we we PRON iajs-3911 197 5 select select VERB iajs-3911 197 6 πœ† πœ† PRON iajs-3911 197 7 = = SYM iajs-3911 197 8 0.5,1,1.5 0.5,1,1.5 NOUN iajs-3911 197 9 , , PUNCT iajs-3911 197 10 these these DET iajs-3911 197 11 values value NOUN iajs-3911 197 12 were be AUX iajs-3911 197 13 selected select VERB iajs-3911 197 14 at at ADP iajs-3911 197 15 random random ADJ iajs-3911 197 16 . . PUNCT iajs-3911 198 1   NOUN iajs-3911 198 2 n n CCONJ iajs-3911 198 3 = = PRON iajs-3911 198 4 represent represent VERB iajs-3911 198 5 the the DET iajs-3911 198 6 replicate replicate NOUN iajs-3911 198 7 of of ADP iajs-3911 198 8 experiment experiment NOUN iajs-3911 198 9 then then ADV iajs-3911 198 10 n=1000 n=1000 PROPN iajs-3911 198 11 ο‚· ο‚· NOUN iajs-3911 198 12 𝐹(𝑑 𝐹(𝑑 NUM iajs-3911 198 13 ) ) PUNCT iajs-3911 198 14 = = SYM iajs-3911 198 15 1 1 NUM iajs-3911 198 16 βˆ’ βˆ’ NOUN iajs-3911 198 17 𝑆(𝑑 𝑆(𝑑 ADJ iajs-3911 198 18 ) ) PUNCT iajs-3911 198 19 = = SYM iajs-3911 198 20 1 1 NUM iajs-3911 198 21 βˆ’ βˆ’ PROPN iajs-3911 198 22 π‘’βˆ’(𝛼𝑑+ π‘’βˆ’(𝛼𝑑+ NUM iajs-3911 198 23 πœ† πœ† DET iajs-3911 198 24 2 2 NUM iajs-3911 198 25 𝑑2 𝑑2 NOUN iajs-3911 198 26 ) ) PUNCT iajs-3911 198 27 𝑒 𝑒 NOUN iajs-3911 198 28 = = SYM iajs-3911 198 29 1 1 NUM iajs-3911 198 30 βˆ’ βˆ’ PROPN iajs-3911 198 31 π‘’βˆ’(𝛼𝑑+ π‘’βˆ’(𝛼𝑑+ NUM iajs-3911 198 32 πœ† πœ† DET iajs-3911 198 33 2 2 NUM iajs-3911 198 34 𝑑2 𝑑2 NOUN iajs-3911 198 35 ) ) PUNCT iajs-3911 198 36 1 1 NUM iajs-3911 198 37 βˆ’ βˆ’ PROPN iajs-3911 198 38 𝑒 𝑒 X iajs-3911 198 39 = = PUNCT iajs-3911 198 40 π‘’βˆ’(𝛼𝑑+ π‘’βˆ’(𝛼𝑑+ PROPN iajs-3911 198 41 πœ† πœ† DET iajs-3911 198 42 2 2 NUM iajs-3911 198 43 𝑑2 𝑑2 NOUN iajs-3911 198 44 ) ) PUNCT iajs-3911 199 1 ln(1 ln(1 ADP iajs-3911 199 2 βˆ’ βˆ’ NUM iajs-3911 199 3 𝑒 𝑒 X iajs-3911 199 4 ) ) PUNCT iajs-3911 199 5 = = SYM iajs-3911 199 6 βˆ’ βˆ’ PROPN iajs-3911 199 7 ( ( PUNCT iajs-3911 199 8 𝛼𝑑 𝛼𝑑 ADP iajs-3911 199 9 + + NOUN iajs-3911 199 10 πœ† πœ† DET iajs-3911 199 11 2 2 NUM iajs-3911 199 12 𝑑2 𝑑2 NOUN iajs-3911 199 13 ) ) PUNCT iajs-3911 200 1 ln(1 ln(1 ADP iajs-3911 200 2 βˆ’ βˆ’ NUM iajs-3911 200 3 𝑒 𝑒 X iajs-3911 200 4 ) ) PUNCT iajs-3911 200 5 + + NOUN iajs-3911 200 6 𝛼𝑑 𝛼𝑑 PROPN iajs-3911 200 7 + + CCONJ iajs-3911 200 8 πœ† πœ† DET iajs-3911 200 9 2 2 NUM iajs-3911 200 10 𝑑2 𝑑2 NOUN iajs-3911 200 11 = = NOUN iajs-3911 200 12 0 0 NUM iajs-3911 201 1 π‘Ž π‘Ž X iajs-3911 201 2 = = SYM iajs-3911 201 3 πœ† πœ† ADP iajs-3911 201 4 2 2 NUM iajs-3911 201 5 , , PUNCT iajs-3911 201 6 𝑏 𝑏 PROPN iajs-3911 201 7 = = SYM iajs-3911 201 8 𝛼 𝛼 PROPN iajs-3911 201 9 , , PUNCT iajs-3911 201 10 𝑐 𝑐 NOUN iajs-3911 201 11 = = SYM iajs-3911 201 12 ln(1 ln(1 NOUN iajs-3911 201 13 βˆ’ βˆ’ NUM iajs-3911 201 14 𝑒 𝑒 X iajs-3911 201 15 ) ) PUNCT iajs-3911 201 16 𝑑1,2 𝑑1,2 ADJ iajs-3911 201 17 = = SYM iajs-3911 201 18 βˆ’π‘Β±βˆšπ‘2βˆ’4π‘Žπ‘ βˆ’π‘Β±βˆšπ‘2βˆ’4π‘Žπ‘ ADJ iajs-3911 201 19 2π‘Ž 2π‘Ž NUM iajs-3911 201 20 𝑑 𝑑 PROPN iajs-3911 201 21 = = X iajs-3911 201 22 βˆ’π›ΌΒ±βˆšπ›Ό2βˆ’2πœ† βˆ’π›ΌΒ±βˆšπ›Ό2βˆ’2πœ† PROPN iajs-3911 201 23 ln(1βˆ’π‘’ ln(1βˆ’π‘’ PROPN iajs-3911 201 24 ) ) PUNCT iajs-3911 202 1 πœ† πœ† ADP iajs-3911 202 2 ο‚· ο‚· PRON iajs-3911 202 3 we we PRON iajs-3911 202 4 find find VERB iajs-3911 202 5 absolut absolut ADJ iajs-3911 202 6 error error NOUN iajs-3911 202 7 value value NOUN iajs-3911 202 8 as as SCONJ iajs-3911 202 9 follows follow VERB iajs-3911 202 10 : : PUNCT iajs-3911 202 11 πœ™π›Ό πœ™π›Ό INTJ iajs-3911 202 12 = = SYM iajs-3911 202 13 𝑀𝑖𝑛| 𝑀𝑖𝑛| PROPN iajs-3911 202 14 οΏ½ οΏ½ PROPN iajs-3911 202 15 Μ‚ Μ‚ VERB iajs-3911 202 16 οΏ½ οΏ½ NOUN iajs-3911 202 17 𝑖 𝑖 SYM iajs-3911 202 18 βˆ’ βˆ’ PROPN iajs-3911 202 19 𝛼| 𝛼| NOUN iajs-3911 202 20 , , PUNCT iajs-3911 202 21 πœ™πœ† πœ™πœ† NOUN iajs-3911 202 22 = = SYM iajs-3911 202 23 𝑀𝑖𝑛| 𝑀𝑖𝑛| PROPN iajs-3911 202 24 οΏ½ οΏ½ PROPN iajs-3911 202 25 Μ‚ Μ‚ VERB iajs-3911 202 26 οΏ½ οΏ½ PROPN iajs-3911 202 27 𝑖 𝑖 PART iajs-3911 202 28 βˆ’ βˆ’ PROPN iajs-3911 202 29 πœ†| πœ†| NOUN iajs-3911 202 30 ο‚· ο‚· NOUN iajs-3911 202 31 we we PRON iajs-3911 202 32 find find VERB iajs-3911 202 33 mean mean ADJ iajs-3911 202 34 squares square NOUN iajs-3911 202 35 errors error NOUN iajs-3911 202 36 for for ADP iajs-3911 202 37 parameter parameter NOUN iajs-3911 202 38 ( ( PUNCT iajs-3911 202 39 𝛼 𝛼 NOUN iajs-3911 202 40 ) ) PUNCT iajs-3911 202 41 and and CCONJ iajs-3911 202 42 parameter(πœ† parameter(πœ† PROPN iajs-3911 202 43 ) ) PUNCT iajs-3911 202 44 . . PUNCT iajs-3911 203 1 𝑀𝑆𝐸[𝑆(𝑑 𝑀𝑆𝐸[𝑆(𝑑 VERB iajs-3911 203 2 ) ) PUNCT iajs-3911 203 3 ] ] PUNCT iajs-3911 204 1 = = PUNCT iajs-3911 204 2 βˆ‘ βˆ‘ PUNCT iajs-3911 204 3 [ [ X iajs-3911 204 4 οΏ½ οΏ½ NOUN iajs-3911 204 5 Μ‚ Μ‚ SYM iajs-3911 204 6 οΏ½ οΏ½ NOUN iajs-3911 204 7 (𝑑𝑖)βˆ’π‘†(𝑑𝑖 (𝑑𝑖)βˆ’π‘†(𝑑𝑖 NOUN iajs-3911 204 8 ) ) PUNCT iajs-3911 204 9 ] ] PUNCT iajs-3911 204 10 2 2 NUM iajs-3911 204 11 𝑁 𝑁 PROPN iajs-3911 204 12 𝑁 𝑁 PROPN iajs-3911 204 13 𝐼=1 𝐼=1 PROPN iajs-3911 204 14 , , PUNCT iajs-3911 204 15 𝑀𝑆𝐸[𝛼 𝑀𝑆𝐸[𝛼 NOUN iajs-3911 204 16 ] ] PUNCT iajs-3911 204 17 = = PUNCT iajs-3911 204 18 βˆ‘ βˆ‘ PUNCT iajs-3911 204 19 [ [ X iajs-3911 204 20 οΏ½ οΏ½ NOUN iajs-3911 204 21 Μ‚ Μ‚ SYM iajs-3911 204 22 οΏ½ οΏ½ NOUN iajs-3911 204 23 π‘–βˆ’π›Ό]2 π‘–βˆ’π›Ό]2 X iajs-3911 204 24 𝑁 𝑁 PROPN iajs-3911 204 25 𝑁 𝑁 PROPN iajs-3911 204 26 𝐼=1 𝐼=1 PROPN iajs-3911 204 27 , , PUNCT iajs-3911 204 28 𝑀𝑆𝐸[πœ† 𝑀𝑆𝐸[πœ† NOUN iajs-3911 204 29 ] ] X iajs-3911 204 30 = = PUNCT iajs-3911 204 31 βˆ‘ βˆ‘ PUNCT iajs-3911 204 32 [ [ X iajs-3911 204 33 οΏ½ οΏ½ NOUN iajs-3911 204 34 Μ‚ Μ‚ SYM iajs-3911 204 35 οΏ½ οΏ½ NOUN iajs-3911 204 36 π‘–βˆ’πœ† π‘–βˆ’πœ† NOUN iajs-3911 204 37 ] ] PUNCT iajs-3911 204 38 2 2 NUM iajs-3911 204 39 𝑁 𝑁 PROPN iajs-3911 204 40 𝑁 𝑁 PROPN iajs-3911 204 41 𝐼=1 𝐼=1 NUM iajs-3911 204 42 4 4 NUM iajs-3911 204 43 . . PUNCT iajs-3911 204 44 numerical numerical PROPN iajs-3911 204 45 results result NOUN iajs-3911 204 46 the the DET iajs-3911 204 47 numerical numerical ADJ iajs-3911 204 48 results result NOUN iajs-3911 204 49 for for ADP iajs-3911 204 50 the the DET iajs-3911 204 51 simulation simulation NOUN iajs-3911 204 52 approach approach NOUN iajs-3911 204 53 are be AUX iajs-3911 204 54 exhibited exhibit VERB iajs-3911 204 55 in in ADP iajs-3911 204 56 the the DET iajs-3911 204 57 following follow VERB iajs-3911 204 58 tables table NOUN iajs-3911 204 59 after after SCONJ iajs-3911 204 60 the the DET iajs-3911 204 61 simulation simulation NOUN iajs-3911 204 62 procedure procedure NOUN iajs-3911 204 63 has have AUX iajs-3911 204 64 been be AUX iajs-3911 204 65 used use VERB iajs-3911 204 66 to to PART iajs-3911 204 67 determine determine VERB iajs-3911 204 68 the the DET iajs-3911 204 69 parameter parameter NOUN iajs-3911 204 70 estimation estimation NOUN iajs-3911 204 71 , , PUNCT iajs-3911 204 72 reliability reliability NOUN iajs-3911 204 73 function function NOUN iajs-3911 204 74 , , PUNCT iajs-3911 204 75 and and CCONJ iajs-3911 204 76 mean mean VERB iajs-3911 204 77 square square ADJ iajs-3911 204 78 error error NOUN iajs-3911 204 79 technique technique NOUN iajs-3911 204 80 . . PUNCT iajs-3911 205 1 with with ADP iajs-3911 205 2 a a DET iajs-3911 205 3 1000 1000 NUM iajs-3911 205 4 iteration iteration NOUN iajs-3911 205 5 rate rate NOUN iajs-3911 205 6 , , PUNCT iajs-3911 205 7 the the DET iajs-3911 205 8 matlab matlab PROPN iajs-3911 205 9 software software NOUN iajs-3911 205 10 employed employ VERB iajs-3911 205 11 the the DET iajs-3911 205 12 monte monte PROPN iajs-3911 205 13 carlo carlo PROPN iajs-3911 205 14 methodology methodology NOUN iajs-3911 205 15 for for ADP iajs-3911 205 16 the the DET iajs-3911 205 17 simulation simulation NOUN iajs-3911 205 18 and and CCONJ iajs-3911 205 19 the the DET iajs-3911 205 20 newton newton PROPN iajs-3911 205 21 - - PUNCT iajs-3911 205 22 raphson raphson PROPN iajs-3911 205 23 method method NOUN iajs-3911 205 24 for for ADP iajs-3911 205 25 the the DET iajs-3911 205 26 numerical numerical ADJ iajs-3911 205 27 solution solution NOUN iajs-3911 205 28 . . PUNCT iajs-3911 206 1 as as SCONJ iajs-3911 206 2 shown show VERB iajs-3911 206 3 in in ADP iajs-3911 206 4 table table NOUN iajs-3911 206 5 ( ( PUNCT iajs-3911 206 6 1 1 NUM iajs-3911 206 7 , , PUNCT iajs-3911 206 8 2 2 NUM iajs-3911 206 9 , , PUNCT iajs-3911 206 10 3 3 NUM iajs-3911 206 11 , , PUNCT iajs-3911 206 12 4 4 NUM iajs-3911 206 13 , , PUNCT iajs-3911 206 14 5 5 NUM iajs-3911 206 15 ) ) PUNCT iajs-3911 206 16 . . PUNCT iajs-3911 207 1 noting note VERB iajs-3911 207 2 from from ADP iajs-3911 207 3 the the DET iajs-3911 207 4 table table NOUN iajs-3911 207 5 1 1 NUM iajs-3911 207 6 that that PRON iajs-3911 207 7 absolut absolut PROPN iajs-3911 207 8 error error NOUN iajs-3911 207 9 values value NOUN iajs-3911 207 10 of of ADP iajs-3911 207 11 parameter parameter NOUN iajs-3911 207 12 ( ( PUNCT iajs-3911 207 13 𝛼)for 𝛼)for NOUN iajs-3911 207 14 lindely lindely ADV iajs-3911 207 15 approximation approximation NOUN iajs-3911 207 16 estimate estimate NOUN iajs-3911 207 17 values value NOUN iajs-3911 207 18 method method NOUN iajs-3911 207 19 are be AUX iajs-3911 207 20 the the DET iajs-3911 207 21 best good ADJ iajs-3911 207 22 for for ADP iajs-3911 207 23 the the DET iajs-3911 207 24 tierney tierney PROPN iajs-3911 207 25 and and CCONJ iajs-3911 207 26 kadane kadane PROPN iajs-3911 207 27 approximation approximation NOUN iajs-3911 207 28 estimation estimation NOUN iajs-3911 207 29 method method NOUN iajs-3911 207 30 . . PUNCT iajs-3911 208 1 noting note VERB iajs-3911 208 2 from from ADP iajs-3911 208 3 the the DET iajs-3911 208 4 table table NOUN iajs-3911 208 5 2 2 NUM iajs-3911 208 6 that that PRON iajs-3911 208 7 absolut absolut PROPN iajs-3911 208 8 error error NOUN iajs-3911 208 9 values value NOUN iajs-3911 208 10 of of ADP iajs-3911 208 11 parameter parameter NOUN iajs-3911 208 12 ( ( PUNCT iajs-3911 208 13 πœ†)for πœ†)for NOUN iajs-3911 208 14 lindely lindely ADV iajs-3911 208 15 approximation approximation NOUN iajs-3911 208 16 estimate estimate NOUN iajs-3911 208 17 values value NOUN iajs-3911 208 18 method method NOUN iajs-3911 208 19 are be AUX iajs-3911 208 20 the the DET iajs-3911 208 21 best good ADJ iajs-3911 208 22 for for ADP iajs-3911 208 23 the the DET iajs-3911 208 24 tierney tierney PROPN iajs-3911 208 25 and and CCONJ iajs-3911 208 26 kadane kadane PROPN iajs-3911 208 27 approximation approximation NOUN iajs-3911 208 28 estimation estimation NOUN iajs-3911 208 29 method method NOUN iajs-3911 208 30 . . PUNCT iajs-3911 209 1 noting note VERB iajs-3911 209 2 from from ADP iajs-3911 209 3 the the DET iajs-3911 209 4 table table NOUN iajs-3911 209 5 3 3 NUM iajs-3911 209 6 that that PRON iajs-3911 209 7 mean mean VERB iajs-3911 209 8 square square ADJ iajs-3911 209 9 error error NOUN iajs-3911 209 10 ( ( PUNCT iajs-3911 209 11 𝛼 𝛼 NOUN iajs-3911 209 12 ) ) PUNCT iajs-3911 209 13 for for ADP iajs-3911 209 14 lindely lindely ADV iajs-3911 209 15 approximation approximation NOUN iajs-3911 209 16 estimate estimate NOUN iajs-3911 209 17 values value NOUN iajs-3911 209 18 method method NOUN iajs-3911 209 19 are be AUX iajs-3911 209 20 the the DET iajs-3911 209 21 best good ADJ iajs-3911 209 22 for for ADP iajs-3911 209 23 the the DET iajs-3911 209 24 tierney tierney PROPN iajs-3911 209 25 and and CCONJ iajs-3911 209 26 kadane kadane PROPN iajs-3911 209 27 approximation approximation NOUN iajs-3911 209 28 estimation estimation NOUN iajs-3911 209 29 method method NOUN iajs-3911 209 30 . . PUNCT iajs-3911 210 1 noting note VERB iajs-3911 210 2 from from ADP iajs-3911 210 3 the the DET iajs-3911 210 4 table table NOUN iajs-3911 210 5 4 4 NUM iajs-3911 210 6 . . PUNCT iajs-3911 210 7 that that PRON iajs-3911 210 8 mean mean VERB iajs-3911 210 9 square square ADJ iajs-3911 210 10 error error NOUN iajs-3911 210 11 of of ADP iajs-3911 210 12 survival survival NOUN iajs-3911 210 13 function function NOUN iajs-3911 210 14 for for ADP iajs-3911 210 15 lindely lindely ADV iajs-3911 210 16 approximation approximation NOUN iajs-3911 210 17 estimate estimate NOUN iajs-3911 210 18 values value NOUN iajs-3911 210 19 method method NOUN iajs-3911 210 20 are be AUX iajs-3911 210 21 the the DET iajs-3911 210 22 best good ADJ iajs-3911 210 23 for for ADP iajs-3911 210 24 the the DET iajs-3911 210 25 tierney tierney PROPN iajs-3911 210 26 and and CCONJ iajs-3911 210 27 kadane kadane PROPN iajs-3911 210 28 approximation approximation NOUN iajs-3911 210 29 estimation estimation NOUN iajs-3911 210 30 method method NOUN iajs-3911 210 31 . . PUNCT iajs-3911 211 1 noting note VERB iajs-3911 211 2 from from ADP iajs-3911 211 3 the the DET iajs-3911 211 4 table table NOUN iajs-3911 211 5 5 5 NUM iajs-3911 211 6 that that PRON iajs-3911 211 7 mean mean VERB iajs-3911 211 8 square square ADJ iajs-3911 211 9 error error NOUN iajs-3911 211 10 of of ADP iajs-3911 211 11 parameter parameter NOUN iajs-3911 211 12 ( ( PUNCT iajs-3911 211 13 πœ† πœ† NOUN iajs-3911 211 14 ) ) PUNCT iajs-3911 211 15 for for ADP iajs-3911 211 16 lindely lindely ADV iajs-3911 211 17 approximation approximation NOUN iajs-3911 211 18 estimate estimate NOUN iajs-3911 211 19 values value NOUN iajs-3911 211 20 method method NOUN iajs-3911 211 21 are be AUX iajs-3911 211 22 the the DET iajs-3911 211 23 best good ADJ iajs-3911 211 24 for for ADP iajs-3911 211 25 the the DET iajs-3911 211 26 tierney tierney PROPN iajs-3911 211 27 and and CCONJ iajs-3911 211 28 kadane kadane PROPN iajs-3911 211 29 approximation approximation NOUN iajs-3911 211 30 estimation estimation NOUN iajs-3911 211 31 method method NOUN iajs-3911 211 32 ihjpas ihjpas PROPN iajs-3911 211 33 . . 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0.5 0.5 NUM iajs-3911 215 127 0.5 0.5 NUM iajs-3911 215 128 50 50 NUM iajs-3911 215 129 0.499963 0.499963 NUM iajs-3911 215 130 0.508847 0.508847 NUM iajs-3911 215 131 3.67e-05 3.67e-05 NUM iajs-3911 215 132 0.5 0.5 NUM iajs-3911 215 133 1 1 NUM iajs-3911 215 134 10 10 NUM iajs-3911 215 135 1.016357 1.016357 NUM iajs-3911 215 136 0.963378 0.963378 NUM iajs-3911 215 137 0.016357 0.016357 NUM iajs-3911 215 138 0.5 0.5 NUM iajs-3911 215 139 1 1 NUM iajs-3911 215 140 20 20 NUM iajs-3911 215 141 1.004066 1.004066 NUM iajs-3911 215 142 1.010583 1.010583 NUM iajs-3911 215 143 0.004066 0.004066 NUM iajs-3911 215 144 0.5 0.5 NUM iajs-3911 215 145 1 1 NUM iajs-3911 215 146 30 30 NUM iajs-3911 215 147 1.000015 1.000015 NUM iajs-3911 215 148 1.066669 1.066669 NUM iajs-3911 215 149 1.47e-05 1.47e-05 NUM iajs-3911 215 150 0.5 0.5 NUM iajs-3911 215 151 1 1 NUM iajs-3911 215 152 50 50 NUM iajs-3911 215 153 0.999995 0.999995 NUM iajs-3911 215 154 1.110389 1.110389 NUM iajs-3911 215 155 5.04e-06 5.04e-06 NUM iajs-3911 215 156 0.5 0.5 NUM iajs-3911 215 157 1.5 1.5 NUM iajs-3911 215 158 10 10 NUM iajs-3911 215 159 1.543717 1.543717 NUM iajs-3911 215 160 1.476047 1.476047 NUM iajs-3911 215 161 0.023953 0.023953 NUM iajs-3911 215 162 0.5 0.5 NUM iajs-3911 215 163 1.5 1.5 NUM iajs-3911 215 164 20 20 NUM iajs-3911 215 165 1.495319 1.495319 NUM iajs-3911 215 166 1.536033 1.536033 NUM iajs-3911 215 167 0.004681 0.004681 NUM iajs-3911 215 168 0.5 0.5 NUM iajs-3911 215 169 1.5 1.5 NUM iajs-3911 215 170 30 30 NUM iajs-3911 215 171 1.500462 1.500462 NUM iajs-3911 215 172 1.220021 1.220021 NUM iajs-3911 215 173 0.000462 0.000462 NUM iajs-3911 215 174 0.5 0.5 NUM iajs-3911 215 175 1.5 1.5 NUM iajs-3911 215 176 50 50 NUM iajs-3911 215 177 1.500013 1.500013 NUM iajs-3911 215 178 1.543239 1.543239 NUM iajs-3911 215 179 1.34e-05 1.34e-05 NUM iajs-3911 215 180 0.75 0.75 NUM iajs-3911 215 181 0.5 0.5 NUM iajs-3911 215 182 10 10 NUM iajs-3911 215 183 0.52599 0.52599 NUM iajs-3911 215 184 0.370504 0.370504 NUM iajs-3911 215 185 0.02599 0.02599 NUM iajs-3911 215 186 0.75 0.75 NUM iajs-3911 215 187 0.5 0.5 NUM iajs-3911 215 188 20 20 NUM iajs-3911 215 189 0.50068 0.50068 NUM iajs-3911 215 190 0.551145 0.551145 NUM iajs-3911 215 191 0.00068 0.00068 NUM iajs-3911 215 192 0.75 0.75 NUM iajs-3911 215 193 0.5 0.5 NUM iajs-3911 215 194 30 30 NUM iajs-3911 215 195 0.499906 0.499906 NUM iajs-3911 215 196 0.489555 0.489555 NUM iajs-3911 215 197 9.44e-05 9.44e-05 NUM iajs-3911 215 198 0.75 0.75 NUM iajs-3911 215 199 0.5 0.5 NUM iajs-3911 215 200 50 50 NUM iajs-3911 215 201 0.499992 0.499992 NUM iajs-3911 215 202 0.499552 0.499552 NUM iajs-3911 215 203 8.31e-06 8.31e-06 NUM iajs-3911 215 204 0.75 0.75 NUM iajs-3911 215 205 1 1 NUM iajs-3911 215 206 10 10 NUM iajs-3911 215 207 1.0467 1.0467 NUM iajs-3911 215 208 1.436493 1.436493 NUM iajs-3911 215 209 0.0467 0.0467 NUM iajs-3911 215 210 0.75 0.75 NUM iajs-3911 215 211 1 1 NUM iajs-3911 215 212 20 20 NUM iajs-3911 215 213 0.995807 0.995807 NUM iajs-3911 215 214 0.783461 0.783461 NUM iajs-3911 215 215 0.004193 0.004193 NUM iajs-3911 215 216 0.75 0.75 NUM iajs-3911 215 217 1 1 NUM iajs-3911 215 218 30 30 NUM iajs-3911 215 219 1.000245 1.000245 NUM iajs-3911 215 220 1.196793 1.196793 NUM iajs-3911 215 221 0.000245 0.000245 NUM iajs-3911 215 222 0.75 0.75 NUM iajs-3911 215 223 1 1 NUM iajs-3911 215 224 50 50 NUM iajs-3911 215 225 0.999999 0.999999 NUM iajs-3911 215 226 0.990902 0.990902 NUM iajs-3911 215 227 1.16e-06 1.16e-06 NUM iajs-3911 215 228 0.75 0.75 NUM iajs-3911 215 229 1.5 1.5 NUM iajs-3911 215 230 10 10 NUM iajs-3911 215 231 1.545809 1.545809 NUM iajs-3911 215 232 1.351652 1.351652 NUM iajs-3911 215 233 0.045809 0.045809 NUM iajs-3911 215 234 0.75 0.75 NUM iajs-3911 215 235 1.5 1.5 NUM iajs-3911 215 236 20 20 NUM iajs-3911 215 237 1.498723 1.498723 NUM iajs-3911 215 238 1.640125 1.640125 NUM iajs-3911 215 239 0.001277 0.001277 NUM iajs-3911 215 240 0.75 0.75 NUM iajs-3911 215 241 1.5 1.5 NUM iajs-3911 215 242 30 30 NUM iajs-3911 215 243 1.500127 1.500127 NUM iajs-3911 215 244 1.439778 1.439778 NUM iajs-3911 215 245 0.000127 0.000127 NUM iajs-3911 215 246 0.75 0.75 NUM iajs-3911 215 247 1.5 1.5 NUM iajs-3911 215 248 50 50 NUM iajs-3911 215 249 1.499983 1.499983 NUM iajs-3911 215 250 1.298486 1.298486 NUM iajs-3911 215 251 1.71e-05 1.71e-05 NUM iajs-3911 215 252 . . PUNCT iajs-3911 216 1 ihjpas ihjpas PROPN iajs-3911 216 2 . . PUNCT iajs-3911 217 1 2025,38(2 2025,38(2 PROPN iajs-3911 217 2 ) ) PUNCT iajs-3911 217 3 413 413 NUM iajs-3911 217 4 table table NOUN iajs-3911 217 5 3 3 NUM iajs-3911 217 6 . . PUNCT iajs-3911 217 7 represent represent VERB iajs-3911 217 8 the the DET iajs-3911 217 9 mse mse NOUN iajs-3911 217 10 for for ADP iajs-3911 217 11 parameter parameter NOUN iajs-3911 217 12 ( ( PUNCT iajs-3911 217 13 𝛼 𝛼 NOUN iajs-3911 217 14 ) ) PUNCT iajs-3911 217 15 of of ADP iajs-3911 217 16 all all DET iajs-3911 217 17 bayesian bayesian NOUN iajs-3911 217 18 method method VERB iajs-3911 217 19 𝛼 𝛼 PROPN iajs-3911 217 20 πœ† πœ† PROPN iajs-3911 217 21 𝑛 𝑛 PRON iajs-3911 217 22 𝑀𝑆𝐸 𝑀𝑆𝐸 PROPN iajs-3911 217 23 οΏ½ οΏ½ PROPN iajs-3911 217 24 Μ‚ Μ‚ VERB iajs-3911 217 25 οΏ½ οΏ½ NOUN iajs-3911 217 26 𝐿𝐴𝐸 𝐿𝐴𝐸 PROPN iajs-3911 217 27 𝑀𝑆𝐸 𝑀𝑆𝐸 PROPN iajs-3911 217 28 οΏ½ οΏ½ PROPN iajs-3911 217 29 Μ‚ Μ‚ NOUN iajs-3911 217 30 οΏ½ οΏ½ NOUN iajs-3911 217 31 𝑇𝐾𝐴𝐸 𝑇𝐾𝐴𝐸 NOUN iajs-3911 217 32 min min NOUN iajs-3911 217 33 0.25 0.25 NUM iajs-3911 217 34 0.5 0.5 NUM iajs-3911 217 35 10 10 NUM iajs-3911 217 36 0.061014 0.061014 NUM iajs-3911 217 37 0.07584 0.07584 NUM iajs-3911 217 38 0.17413 0.17413 NUM iajs-3911 217 39 0.25 0.25 NUM iajs-3911 217 40 0.5 0.5 NUM iajs-3911 217 41 20 20 NUM iajs-3911 217 42 4.11e-06 4.11e-06 NUM iajs-3911 217 43 1.91e-05 1.91e-05 NUM iajs-3911 217 44 4.11e-06 4.11e-06 NUM iajs-3911 217 45 0.25 0.25 NUM iajs-3911 217 46 0.5 0.5 NUM iajs-3911 217 47 30 30 NUM iajs-3911 217 48 2.53e-07 2.53e-07 NUM iajs-3911 217 49 1.5e-07 1.5e-07 NUM iajs-3911 217 50 9.37e-08 9.37e-08 NUM iajs-3911 217 51 0.25 0.25 NUM iajs-3911 217 52 0.5 0.5 NUM iajs-3911 217 53 50 50 NUM iajs-3911 217 54 7.47e-10 7.47e-10 NUM iajs-3911 217 55 2.04e-08 2.04e-08 NUM iajs-3911 217 56 7.47e-10 7.47e-10 NUM iajs-3911 217 57 0.25 0.25 NUM iajs-3911 217 58 1 1 NUM iajs-3911 217 59 10 10 NUM iajs-3911 217 60 0.002126 0.002126 NUM iajs-3911 217 61 0.042557 0.042557 NUM iajs-3911 218 1 0.002126 0.002126 NUM iajs-3911 218 2 0.25 0.25 NUM iajs-3911 218 3 1 1 NUM iajs-3911 218 4 20 20 NUM iajs-3911 218 5 8.36e-06 8.36e-06 NUM iajs-3911 218 6 0.018076 0.018076 NUM iajs-3911 218 7 8.36e-06 8.36e-06 NUM iajs-3911 218 8 0.25 0.25 NUM iajs-3911 218 9 1 1 NUM iajs-3911 218 10 30 30 NUM iajs-3911 218 11 2.22e-07 2.22e-07 NUM iajs-3911 218 12 0.004964 0.004964 NUM iajs-3911 218 13 2.22e-07 2.22e-07 NUM iajs-3911 218 14 0.25 0.25 NUM iajs-3911 218 15 1 1 NUM iajs-3911 218 16 50 50 NUM iajs-3911 218 17 2.49e-09 2.49e-09 NUM iajs-3911 218 18 0.00025 0.00025 NUM iajs-3911 218 19 2.49e-09 2.49e-09 NUM iajs-3911 218 20 0.25 0.25 NUM iajs-3911 218 21 1.5 1.5 NUM iajs-3911 218 22 10 10 NUM iajs-3911 218 23 0.000907 0.000907 NUM iajs-3911 218 24 0.002617 0.002617 NUM iajs-3911 219 1 0.000907 0.000907 NUM iajs-3911 219 2 0.25 0.25 NUM iajs-3911 219 3 1.5 1.5 NUM iajs-3911 219 4 20 20 NUM iajs-3911 219 5 1.24e-05 1.24e-05 NUM iajs-3911 219 6 0.000428 0.000428 NUM iajs-3911 219 7 1.24e-05 1.24e-05 NUM iajs-3911 219 8 0.25 0.25 NUM iajs-3911 219 9 1.5 1.5 NUM iajs-3911 219 10 30 30 NUM iajs-3911 219 11 1.7e-07 1.7e-07 NUM iajs-3911 219 12 4.21e-06 4.21e-06 NUM iajs-3911 219 13 1.7e-07 1.7e-07 NUM iajs-3911 219 14 0.25 0.25 NUM iajs-3911 219 15 1.5 1.5 NUM iajs-3911 219 16 50 50 NUM iajs-3911 219 17 8.12e-11 8.12e-11 NUM iajs-3911 219 18 0.000194 0.000194 NUM iajs-3911 219 19 8.12e-11 8.12e-11 NUM iajs-3911 219 20 0.5 0.5 NUM iajs-3911 219 21 0.5 0.5 NUM iajs-3911 219 22 10 10 NUM iajs-3911 219 23 0.002175 0.002175 NUM iajs-3911 219 24 0.151484 0.151484 NUM iajs-3911 219 25 0.002175 0.002175 NUM iajs-3911 219 26 0.5 0.5 NUM iajs-3911 219 27 0.5 0.5 NUM iajs-3911 219 28 20 20 NUM iajs-3911 219 29 4.75e-05 4.75e-05 NUM iajs-3911 219 30 0.137914 0.137914 NUM iajs-3911 219 31 4.75e-05 4.75e-05 NUM iajs-3911 219 32 0.5 0.5 NUM iajs-3911 219 33 0.5 0.5 NUM iajs-3911 219 34 30 30 NUM iajs-3911 219 35 2.09e-07 2.09e-07 NUM iajs-3911 219 36 1.4e-08 1.4e-08 NUM iajs-3911 219 37 1.4e-08 1.4e-08 NUM iajs-3911 219 38 0.5 0.5 NUM iajs-3911 219 39 0.5 0.5 NUM iajs-3911 219 40 50 50 NUM iajs-3911 219 41 7.9e-11 7.9e-11 NUM iajs-3911 219 42 0.019993 0.019993 NUM iajs-3911 219 43 7.9e-11 7.9e-11 NUM iajs-3911 219 44 0.5 0.5 NUM iajs-3911 219 45 1 1 NUM iajs-3911 219 46 10 10 NUM iajs-3911 219 47 0.000705 0.000705 NUM iajs-3911 219 48 0.01733 0.01733 NUM iajs-3911 219 49 0.000705 0.000705 NUM iajs-3911 219 50 0.5 0.5 NUM iajs-3911 219 51 1 1 NUM iajs-3911 219 52 20 20 NUM iajs-3911 219 53 1.62e-05 1.62e-05 NUM iajs-3911 219 54 0.073333 0.073333 NUM iajs-3911 219 55 1.62e-05 1.62e-05 NUM iajs-3911 219 56 0.5 0.5 NUM iajs-3911 219 57 1 1 NUM iajs-3911 219 58 30 30 NUM iajs-3911 219 59 5.35e-07 5.35e-07 NUM iajs-3911 219 60 1.63e-05 1.63e-05 NUM iajs-3911 219 61 5.35e-07 5.35e-07 NUM iajs-3911 219 62 0.5 0.5 NUM iajs-3911 219 63 1 1 NUM iajs-3911 219 64 50 50 NUM iajs-3911 219 65 4.62e-10 4.62e-10 NUM iajs-3911 219 66 0.003877 0.003877 NUM iajs-3911 219 67 4.62e-10 4.62e-10 NUM iajs-3911 219 68 0.5 0.5 NUM iajs-3911 219 69 1.5 1.5 NUM iajs-3911 219 70 10 10 NUM iajs-3911 219 71 0.001242 0.001242 NUM iajs-3911 219 72 0.058183 0.058183 NUM iajs-3911 219 73 0.001242 0.001242 NUM iajs-3911 219 74 0.5 0.5 NUM iajs-3911 219 75 1.5 1.5 NUM iajs-3911 219 76 20 20 NUM iajs-3911 219 77 3.03e-05 3.03e-05 NUM iajs-3911 219 78 0.016625 0.016625 NUM iajs-3911 219 79 3.03e-05 3.03e-05 NUM iajs-3911 219 80 0.5 0.5 NUM iajs-3911 219 81 1.5 1.5 NUM iajs-3911 219 82 30 30 NUM iajs-3911 219 83 1.59e-07 1.59e-07 NUM iajs-3911 219 84 0.000364 0.000364 NUM iajs-3911 219 85 1.59e-07 1.59e-07 NUM iajs-3911 219 86 0.5 0.5 NUM iajs-3911 219 87 1.5 1.5 NUM iajs-3911 219 88 50 50 NUM iajs-3911 219 89 4.42e-09 4.42e-09 NUM iajs-3911 219 90 0.015201 0.015201 NUM iajs-3911 219 91 4.42e-09 4.42e-09 NUM iajs-3911 219 92 0.75 0.75 NUM iajs-3911 219 93 0.5 0.5 NUM iajs-3911 219 94 10 10 NUM iajs-3911 219 95 0.002838 0.002838 NUM iajs-3911 219 96 0.309147 0.309147 NUM iajs-3911 219 97 0.002838 0.002838 NUM iajs-3911 219 98 0.75 0.75 NUM iajs-3911 219 99 0.5 0.5 NUM iajs-3911 219 100 20 20 NUM iajs-3911 219 101 2.4e-06 2.4e-06 NUM iajs-3911 219 102 0.000105 0.000105 NUM iajs-3911 219 103 2.4e-06 2.4e-06 NUM iajs-3911 219 104 0.75 0.75 NUM iajs-3911 219 105 0.5 0.5 NUM iajs-3911 219 106 30 30 NUM iajs-3911 219 107 1.28e-07 1.28e-07 NUM iajs-3911 219 108 1.64e-07 1.64e-07 NUM iajs-3911 219 109 1.28e-07 1.28e-07 NUM iajs-3911 219 110 0.75 0.75 NUM iajs-3911 219 111 0.5 0.5 NUM iajs-3911 219 112 50 50 NUM iajs-3911 219 113 7.23e-11 7.23e-11 NUM iajs-3911 219 114 0.078898 0.078898 NUM iajs-3911 219 115 7.23e-11 7.23e-11 NUM iajs-3911 219 116 0.75 0.75 NUM iajs-3911 219 117 1 1 NUM iajs-3911 219 118 10 10 NUM iajs-3911 219 119 0.000452 0.000452 NUM iajs-3911 219 120 0.135392 0.135392 NUM iajs-3911 219 121 0.000452 0.000452 NUM iajs-3911 219 122 0.75 0.75 NUM iajs-3911 219 123 1 1 NUM iajs-3911 219 124 20 20 NUM iajs-3911 219 125 1.31e-05 1.31e-05 NUM iajs-3911 219 126 0.04142 0.04142 NUM iajs-3911 219 127 1.31e-05 1.31e-05 NUM iajs-3911 219 128 0.75 0.75 NUM iajs-3911 219 129 1 1 NUM iajs-3911 219 130 30 30 NUM iajs-3911 219 131 7.36e-08 7.36e-08 NUM iajs-3911 219 132 0.061872 0.061872 NUM iajs-3911 219 133 7.36e-08 7.36e-08 NUM iajs-3911 219 134 0.75 0.75 NUM iajs-3911 219 135 1 1 NUM iajs-3911 219 136 50 50 NUM iajs-3911 219 137 1.18e-09 1.18e-09 NUM iajs-3911 219 138 0.084636 0.084636 NUM iajs-3911 219 139 1.18e-09 1.18e-09 NUM iajs-3911 219 140 0.75 0.75 NUM iajs-3911 219 141 1.5 1.5 NUM iajs-3911 219 142 10 10 NUM iajs-3911 219 143 0.000532 0.000532 NUM iajs-3911 219 144 0.147029 0.147029 NUM iajs-3911 219 145 0.000532 0.000532 NUM iajs-3911 219 146 0.75 0.75 NUM iajs-3911 219 147 1.5 1.5 NUM iajs-3911 219 148 20 20 NUM iajs-3911 219 149 1.74e-08 1.74e-08 NUM iajs-3911 219 150 0.040548 0.040548 NUM iajs-3911 219 151 1.74e-08 1.74e-08 NUM iajs-3911 219 152 0.75 0.75 NUM iajs-3911 219 153 1.5 1.5 NUM iajs-3911 219 154 30 30 NUM iajs-3911 219 155 3.63e-07 3.63e-07 NUM iajs-3911 219 156 0.000119 0.000119 NUM iajs-3911 219 157 3.63e-07 3.63e-07 NUM iajs-3911 219 158 0.75 0.75 NUM iajs-3911 219 159 1.5 1.5 NUM iajs-3911 219 160 50 50 NUM iajs-3911 219 161 4.55e-09 4.55e-09 NUM iajs-3911 219 162 0.000387 0.000387 NUM iajs-3911 219 163 4.55e-09 4.55e-09 NUM iajs-3911 219 164 ihjpas ihjpa NOUN iajs-3911 219 165 . . PUNCT iajs-3911 220 1 2025,38(2 2025,38(2 NOUN iajs-3911 220 2 ) ) PUNCT iajs-3911 220 3 414 414 NUM iajs-3911 220 4 table table NOUN iajs-3911 220 5 4 4 NUM iajs-3911 220 6 . . PUNCT iajs-3911 220 7 represent represent VERB iajs-3911 220 8 the the DET iajs-3911 220 9 mse mse NOUN iajs-3911 220 10 for for ADP iajs-3911 220 11 parameter parameter NOUN iajs-3911 220 12 ( ( PUNCT iajs-3911 220 13 πœ† πœ† NOUN iajs-3911 220 14 ) ) PUNCT iajs-3911 220 15 of of ADP iajs-3911 220 16 all all DET iajs-3911 220 17 bayesian bayesian NOUN iajs-3911 220 18 method method VERB iajs-3911 220 19 𝛼 𝛼 PROPN iajs-3911 220 20 πœ† πœ† PROPN iajs-3911 220 21 𝑛 𝑛 PRON iajs-3911 220 22 𝑀𝑆𝐸 𝑀𝑆𝐸 PROPN iajs-3911 220 23 οΏ½ οΏ½ PROPN iajs-3911 220 24 Μ‚ Μ‚ VERB iajs-3911 220 25 οΏ½ οΏ½ NOUN iajs-3911 220 26 𝐿𝐴𝐸 𝐿𝐴𝐸 PROPN iajs-3911 220 27 𝑀𝑆𝐸 𝑀𝑆𝐸 PROPN iajs-3911 220 28 οΏ½ οΏ½ PROPN iajs-3911 220 29 Μ‚ Μ‚ VERB iajs-3911 220 30 οΏ½ οΏ½ NOUN iajs-3911 220 31 𝑇𝐾𝐴𝐸 𝑇𝐾𝐴𝐸 PROPN iajs-3911 220 32 π‘šπ‘–π‘› π‘šπ‘–π‘› NOUN iajs-3911 220 33 0.25 0.25 NUM iajs-3911 220 34 0.5 0.5 NUM iajs-3911 220 35 10 10 NUM iajs-3911 220 36 0.000858 0.000858 NUM iajs-3911 220 37 0.031695 0.031695 NUM iajs-3911 220 38 0.000858 0.000858 NUM iajs-3911 220 39 0.25 0.25 NUM iajs-3911 220 40 0.5 0.5 NUM iajs-3911 220 41 20 20 NUM iajs-3911 220 42 1.5e-06 1.5e-06 NUM iajs-3911 220 43 0.01405 0.01405 NUM iajs-3911 221 1 1.5e-06 1.5e-06 NUM iajs-3911 221 2 0.25 0.25 NUM iajs-3911 221 3 0.5 0.5 NUM iajs-3911 221 4 30 30 NUM iajs-3911 221 5 1.69e-07 1.69e-07 NUM iajs-3911 221 6 0.006272 0.006272 NUM iajs-3911 221 7 1.69e-07 1.69e-07 NUM iajs-3911 221 8 0.25 0.25 NUM iajs-3911 221 9 0.5 0.5 NUM iajs-3911 221 10 50 50 NUM iajs-3911 221 11 2.85e-09 2.85e-09 NUM iajs-3911 221 12 0.000979 0.000979 NUM iajs-3911 221 13 2.85e-09 2.85e-09 NUM iajs-3911 221 14 0.25 0.25 NUM iajs-3911 221 15 1 1 NUM iajs-3911 221 16 10 10 NUM iajs-3911 221 17 0.002652 0.002652 NUM iajs-3911 221 18 0.171412 0.171412 NUM iajs-3911 221 19 0.002652 0.002652 NUM iajs-3911 221 20 0.25 0.25 NUM iajs-3911 221 21 1 1 NUM iajs-3911 221 22 20 20 NUM iajs-3911 221 23 5.36e-06 5.36e-06 NUM iajs-3911 221 24 0.009031 0.009031 NUM iajs-3911 221 25 5.36e-06 5.36e-06 NUM iajs-3911 221 26 0.25 0.25 NUM iajs-3911 221 27 1 1 NUM iajs-3911 221 28 30 30 NUM iajs-3911 221 29 1.7e-07 1.7e-07 NUM iajs-3911 221 30 0.005808 0.005808 NUM iajs-3911 221 31 1.7e-07 1.7e-07 NUM iajs-3911 221 32 0.25 0.25 NUM iajs-3911 221 33 1 1 NUM iajs-3911 221 34 50 50 NUM iajs-3911 221 35 1.43e-09 1.43e-09 NUM iajs-3911 221 36 0.025105 0.025105 NUM iajs-3911 221 37 1.43e-09 1.43e-09 NUM iajs-3911 222 1 0.25 0.25 NUM iajs-3911 222 2 1.5 1.5 NUM iajs-3911 222 3 10 10 NUM iajs-3911 222 4 0.000791 0.000791 NUM iajs-3911 222 5 0.72097 0.72097 NUM iajs-3911 222 6 0.000791 0.000791 NUM iajs-3911 222 7 0.25 0.25 NUM iajs-3911 222 8 1.5 1.5 NUM iajs-3911 222 9 20 20 NUM iajs-3911 222 10 1.1e-06 1.1e-06 NUM iajs-3911 222 11 0.031248 0.031248 NUM iajs-3911 222 12 1.1e-06 1.1e-06 NUM iajs-3911 222 13 0.25 0.25 NUM iajs-3911 222 14 1.5 1.5 NUM iajs-3911 222 15 30 30 NUM iajs-3911 222 16 4.33e-07 4.33e-07 NUM iajs-3911 222 17 0.239611 0.239611 NUM iajs-3911 222 18 4.33e-07 4.33e-07 NUM iajs-3911 222 19 0.25 0.25 NUM iajs-3911 222 20 1.5 1.5 NUM iajs-3911 222 21 50 50 NUM iajs-3911 222 22 3.21e-10 3.21e-10 NUM iajs-3911 222 23 0.010335 0.010335 NUM iajs-3911 222 24 3.21e-10 3.21e-10 NUM iajs-3911 222 25 0.5 0.5 NUM iajs-3911 222 26 0.5 0.5 NUM iajs-3911 222 27 10 10 NUM iajs-3911 222 28 0.005259 0.005259 NUM iajs-3911 222 29 0.009682 0.009682 NUM iajs-3911 222 30 0.005259 0.005259 NUM iajs-3911 222 31 0.5 0.5 NUM iajs-3911 222 32 0.5 0.5 NUM iajs-3911 222 33 20 20 NUM iajs-3911 222 34 4.92e-05 4.92e-05 NUM iajs-3911 222 35 0.000478 0.000478 NUM iajs-3911 222 36 4.92e-05 4.92e-05 NUM iajs-3911 222 37 0.5 0.5 NUM iajs-3911 222 38 0.5 0.5 NUM iajs-3911 222 39 30 30 NUM iajs-3911 222 40 8.87e-08 8.87e-08 NUM iajs-3911 222 41 0.012252 0.012252 NUM iajs-3911 222 42 8.87e-08 8.87e-08 NUM iajs-3911 222 43 0.5 0.5 NUM iajs-3911 222 44 0.5 0.5 NUM iajs-3911 222 45 50 50 NUM iajs-3911 222 46 1.48e-09 1.48e-09 NUM iajs-3911 222 47 0.00043 0.00043 NUM iajs-3911 222 48 1.48e-09 1.48e-09 NUM iajs-3911 222 49 0.5 0.5 NUM iajs-3911 222 50 1 1 NUM iajs-3911 222 51 10 10 NUM iajs-3911 222 52 0.004654 0.004654 NUM iajs-3911 222 53 0.002195 0.002195 NUM iajs-3911 222 54 0.002195 0.002195 NUM iajs-3911 222 55 0.5 0.5 NUM iajs-3911 222 56 1 1 NUM iajs-3911 222 57 20 20 NUM iajs-3911 222 58 3.26e-05 3.26e-05 NUM iajs-3911 222 59 0.031042 0.031042 NUM iajs-3911 222 60 3.26e-05 3.26e-05 NUM iajs-3911 222 61 0.5 0.5 NUM iajs-3911 222 62 1 1 NUM iajs-3911 222 63 30 30 NUM iajs-3911 222 64 3.42e-07 3.42e-07 NUM iajs-3911 222 65 0.012912 0.012912 NUM iajs-3911 222 66 3.42e-07 3.42e-07 NUM iajs-3911 222 67 0.5 0.5 NUM iajs-3911 222 68 1 1 NUM iajs-3911 222 69 50 50 NUM iajs-3911 222 70 8.28e-11 8.28e-11 NUM iajs-3911 222 71 0.014289 0.014289 NUM iajs-3911 222 72 8.28e-11 8.28e-11 NUM iajs-3911 222 73 0.5 0.5 NUM iajs-3911 222 74 1.5 1.5 NUM iajs-3911 222 75 10 10 NUM iajs-3911 222 76 0.004483 0.004483 NUM iajs-3911 222 77 0.092447 0.092447 NUM iajs-3911 222 78 0.004483 0.004483 NUM iajs-3911 222 79 0.5 0.5 NUM iajs-3911 222 80 1.5 1.5 NUM iajs-3911 222 81 20 20 NUM iajs-3911 222 82 3.71e-05 3.71e-05 NUM iajs-3911 222 83 0.014191 0.014191 NUM iajs-3911 222 84 3.71e-05 3.71e-05 NUM iajs-3911 222 85 0.5 0.5 NUM iajs-3911 222 86 1.5 1.5 NUM iajs-3911 222 87 30 30 NUM iajs-3911 222 88 4.08e-07 4.08e-07 NUM iajs-3911 222 89 0.11564 0.11564 NUM iajs-3911 222 90 4.08e-07 4.08e-07 NUM iajs-3911 222 91 0.5 0.5 NUM iajs-3911 222 92 1.5 1.5 NUM iajs-3911 222 93 50 50 NUM iajs-3911 222 94 2.63e-10 2.63e-10 NUM iajs-3911 222 95 0.008968 0.008968 NUM iajs-3911 222 96 2.63e-10 2.63e-10 NUM iajs-3911 222 97 0.75 0.75 NUM iajs-3911 222 98 0.5 0.5 NUM iajs-3911 222 99 10 10 NUM iajs-3911 222 100 0.003688 0.003688 NUM iajs-3911 222 101 0.031815 0.031815 NUM iajs-3911 222 102 0.003688 0.003688 NUM iajs-3911 222 103 0.75 0.75 NUM iajs-3911 222 104 0.5 0.5 NUM iajs-3911 222 105 20 20 NUM iajs-3911 222 106 2.55e-05 2.55e-05 NUM iajs-3911 222 107 0.00287 0.00287 NUM iajs-3911 222 108 2.55e-05 2.55e-05 NUM iajs-3911 222 109 0.75 0.75 NUM iajs-3911 222 110 0.5 0.5 NUM iajs-3911 222 111 30 30 NUM iajs-3911 222 112 8.31e-08 8.31e-08 NUM iajs-3911 222 113 0.000111 0.000111 NUM iajs-3911 222 114 8.31e-08 8.31e-08 NUM iajs-3911 222 115 0.75 0.75 NUM iajs-3911 222 116 0.5 0.5 NUM iajs-3911 222 117 50 50 NUM iajs-3911 222 118 8.9e-11 8.9e-11 NUM iajs-3911 222 119 0.000294 0.000294 NUM iajs-3911 222 120 8.9e-11 8.9e-11 NUM iajs-3911 222 121 0.75 0.75 NUM iajs-3911 222 122 1 1 NUM iajs-3911 222 123 10 10 NUM iajs-3911 222 124 0.002613 0.002613 NUM iajs-3911 222 125 0.233707 0.233707 NUM iajs-3911 222 126 0.002613 0.002613 NUM iajs-3911 222 127 0.75 0.75 NUM iajs-3911 222 128 1 1 NUM iajs-3911 222 129 20 20 NUM iajs-3911 222 130 2.49e-05 2.49e-05 NUM iajs-3911 222 131 0.076475 0.076475 NUM iajs-3911 222 132 2.49e-05 2.49e-05 NUM iajs-3911 222 133 0.75 0.75 NUM iajs-3911 222 134 1 1 NUM iajs-3911 222 135 30 30 NUM iajs-3911 222 136 6.02e-08 6.02e-08 NUM iajs-3911 222 137 0.038741 0.038741 NUM iajs-3911 222 138 6.02e-08 6.02e-08 NUM iajs-3911 222 139 0.75 0.75 NUM iajs-3911 222 140 1 1 NUM iajs-3911 222 141 50 50 NUM iajs-3911 222 142 5.13e-11 5.13e-11 NUM iajs-3911 222 143 0.006712 0.006712 NUM iajs-3911 222 144 5.13e-11 5.13e-11 NUM iajs-3911 222 145 0.75 0.75 NUM iajs-3911 222 146 1 1 NUM iajs-3911 222 147 100 100 NUM iajs-3911 222 148 9.85e-12 9.85e-12 NUM iajs-3911 222 149 0.027358 0.027358 NUM iajs-3911 222 150 9.85e-12 9.85e-12 NUM iajs-3911 222 151 0.75 0.75 NUM iajs-3911 222 152 1.5 1.5 NUM iajs-3911 222 153 10 10 NUM iajs-3911 222 154 0.002863 0.002863 NUM iajs-3911 222 155 0.031182 0.031182 NUM iajs-3911 222 156 0.002863 0.002863 NUM iajs-3911 222 157 0.75 0.75 NUM iajs-3911 222 158 1.5 1.5 NUM iajs-3911 222 159 20 20 NUM iajs-3911 222 160 2.1e-06 2.1e-06 NUM iajs-3911 222 161 0.143916 0.143916 NUM iajs-3911 222 162 2.1e-06 2.1e-06 NUM iajs-3911 222 163 0.75 0.75 NUM iajs-3911 222 164 1.5 1.5 NUM iajs-3911 222 165 30 30 NUM iajs-3911 222 166 1.06e-07 1.06e-07 NUM iajs-3911 222 167 0.010499 0.010499 NUM iajs-3911 222 168 1.06e-07 1.06e-07 NUM iajs-3911 222 169 0.75 0.75 NUM iajs-3911 222 170 1.5 1.5 NUM iajs-3911 222 171 50 50 NUM iajs-3911 222 172 4.03e-10 4.03e-10 NUM iajs-3911 222 173 0.07206 0.07206 NUM iajs-3911 222 174 4.03e-10 4.03e-10 NUM iajs-3911 222 175 ihjpas ihjpa NOUN iajs-3911 222 176 . . PUNCT iajs-3911 223 1 2025,38(2 2025,38(2 NOUN iajs-3911 223 2 ) ) PUNCT iajs-3911 223 3 415 415 NUM iajs-3911 223 4 table table NOUN iajs-3911 223 5 5 5 NUM iajs-3911 223 6 . . PUNCT iajs-3911 223 7 represent represent VERB iajs-3911 223 8 the the DET iajs-3911 223 9 mse mse NOUN iajs-3911 223 10 for for ADP iajs-3911 223 11 survival survival NOUN iajs-3911 223 12 function function NOUN iajs-3911 223 13 methods method NOUN iajs-3911 223 14 of of ADP iajs-3911 223 15 all all DET iajs-3911 223 16 bayesian bayesian NOUN iajs-3911 223 17 method method NOUN iajs-3911 223 18 . . PUNCT iajs-3911 224 1 𝛼 𝛼 PROPN iajs-3911 224 2 πœ† πœ† ADP iajs-3911 224 3 𝑛 𝑛 DET iajs-3911 224 4 𝑆𝑀𝑆𝐸𝐿𝐴𝐸 𝑆𝑀𝑆𝐸𝐿𝐴𝐸 PROPN iajs-3911 224 5 𝑆𝑀𝑆𝐸𝑇𝐾𝐴𝐸 𝑆𝑀𝑆𝐸𝑇𝐾𝐴𝐸 NOUN iajs-3911 224 6 min min NOUN iajs-3911 225 1 0.25 0.25 NUM iajs-3911 225 2 0.5 0.5 NUM iajs-3911 225 3 10 10 NUM iajs-3911 225 4 1.79e-05 1.79e-05 NUM iajs-3911 225 5 0.001218 0.001218 NUM iajs-3911 225 6 1.78826e-05 1.78826e-05 NUM iajs-3911 225 7 0.25 0.25 NUM iajs-3911 225 8 0.5 0.5 NUM iajs-3911 225 9 20 20 NUM iajs-3911 225 10 6.69e-08 6.69e-08 NUM iajs-3911 225 11 4.93e-05 4.93e-05 NUM iajs-3911 225 12 6.68907e-08 6.68907e-08 NUM iajs-3911 225 13 0.25 0.25 NUM iajs-3911 225 14 0.5 0.5 NUM iajs-3911 225 15 30 30 NUM iajs-3911 225 16 0.000186 0.000186 NUM iajs-3911 225 17 0.000428 0.000428 NUM iajs-3911 225 18 0.00018582 0.00018582 NUM iajs-3911 225 19 0.25 0.25 NUM iajs-3911 225 20 0.5 0.5 NUM iajs-3911 225 21 50 50 NUM iajs-3911 225 22 2.42e-10 2.42e-10 NUM iajs-3911 225 23 5.92e-05 5.92e-05 NUM iajs-3911 225 24 2.42355e-10 2.42355e-10 NUM iajs-3911 225 25 0.25 0.25 NUM iajs-3911 225 26 1 1 NUM iajs-3911 225 27 10 10 NUM iajs-3911 225 28 3.46e-05 3.46e-05 NUM iajs-3911 225 29 0.000936 0.000936 NUM iajs-3911 225 30 3.45513e-05 3.45513e-05 NUM iajs-3911 225 31 0.25 0.25 NUM iajs-3911 225 32 1 1 NUM iajs-3911 225 33 20 20 NUM iajs-3911 225 34 3.87e-07 3.87e-07 NUM iajs-3911 225 35 0.001142 0.001142 NUM iajs-3911 225 36 3.87255e-07 3.87255e-07 NUM iajs-3911 225 37 0.25 0.25 NUM iajs-3911 225 38 1 1 NUM iajs-3911 225 39 30 30 NUM iajs-3911 225 40 6.94e-06 6.94e-06 NUM iajs-3911 225 41 0.000106 0.000106 NUM iajs-3911 225 42 6.9434e-06 6.9434e-06 NUM iajs-3911 225 43 0.25 0.25 NUM iajs-3911 225 44 1 1 NUM iajs-3911 225 45 50 50 NUM iajs-3911 225 46 2.22e-10 2.22e-10 NUM iajs-3911 225 47 0.000422 0.000422 NUM iajs-3911 225 48 2.21642e-10 2.21642e-10 NUM iajs-3911 225 49 0.25 0.25 NUM iajs-3911 225 50 1.5 1.5 NUM iajs-3911 225 51 10 10 NUM iajs-3911 225 52 8.16e-06 8.16e-06 NUM iajs-3911 225 53 0.013263 0.013263 NUM iajs-3911 225 54 8.15897e-06 8.15897e-06 NUM iajs-3911 225 55 0.25 0.25 NUM iajs-3911 225 56 1.5 1.5 NUM iajs-3911 225 57 20 20 NUM iajs-3911 225 58 3.59e-07 3.59e-07 NUM iajs-3911 225 59 0.000367 0.000367 NUM iajs-3911 225 60 3.59237e-07 3.59237e-07 NUM iajs-3911 225 61 0.25 0.25 NUM iajs-3911 225 62 1.5 1.5 NUM iajs-3911 225 63 30 30 NUM iajs-3911 225 64 1.46e-09 1.46e-09 NUM iajs-3911 225 65 8.85e-05 8.85e-05 NUM iajs-3911 225 66 1.46397e-09 1.46397e-09 NUM iajs-3911 225 67 0.25 0.25 NUM iajs-3911 225 68 1.5 1.5 NUM iajs-3911 225 69 50 50 NUM iajs-3911 225 70 2.01e-12 2.01e-12 NUM iajs-3911 225 71 2.45e-06 2.45e-06 NUM iajs-3911 225 72 2.00982e-12 2.00982e-12 NUM iajs-3911 225 73 0.5 0.5 NUM iajs-3911 225 74 0.5 0.5 NUM iajs-3911 225 75 10 10 NUM iajs-3911 225 76 5.21e-05 5.21e-05 NUM iajs-3911 225 77 0.004192 0.004192 NUM iajs-3911 225 78 5.21315e-05 5.21315e-05 NUM iajs-3911 225 79 0.5 0.5 NUM iajs-3911 225 80 0.5 0.5 NUM iajs-3911 225 81 20 20 NUM iajs-3911 225 82 9.98e-07 9.98e-07 NUM iajs-3911 225 83 0.003911 0.003911 NUM iajs-3911 225 84 9.97916e-07 9.97916e-07 NUM iajs-3911 225 85 0.5 0.5 NUM iajs-3911 225 86 0.5 0.5 NUM iajs-3911 225 87 30 30 NUM iajs-3911 225 88 1.57e-08 1.57e-08 NUM iajs-3911 225 89 5.9e-07 5.9e-07 NUM iajs-3911 225 90 1.57214e-08 1.57214e-08 NUM iajs-3911 225 91 0.5 0.5 NUM iajs-3911 225 92 0.5 0.5 NUM iajs-3911 225 93 50 50 NUM iajs-3911 225 94 2e-11 2e-11 NUM iajs-3911 225 95 0.000716 0.000716 NUM iajs-3911 225 96 2.00342e-11 2.00342e-11 NUM iajs-3911 225 97 0.5 0.5 NUM iajs-3911 225 98 1 1 NUM iajs-3911 225 99 10 10 NUM iajs-3911 225 100 4.54e-06 4.54e-06 NUM iajs-3911 225 101 0.000492 0.000492 NUM iajs-3911 225 102 4.54484e-06 4.54484e-06 NUM iajs-3911 225 103 0.5 0.5 NUM iajs-3911 225 104 1 1 NUM iajs-3911 225 105 20 20 NUM iajs-3911 225 106 1.58e-06 1.58e-06 NUM iajs-3911 225 107 0.003329 0.003329 NUM iajs-3911 225 108 1.57777e-06 1.57777e-06 NUM iajs-3911 225 109 0.5 0.5 NUM iajs-3911 225 110 1 1 NUM 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NUM iajs-3911 225 139 0.5 0.5 NUM iajs-3911 225 140 1.5 1.5 NUM iajs-3911 225 141 50 50 NUM iajs-3911 225 142 5.85e-11 5.85e-11 NUM iajs-3911 225 143 0.000875 0.000875 NUM iajs-3911 225 144 5.84854e-11 5.84854e-11 NUM iajs-3911 225 145 0.75 0.75 NUM iajs-3911 225 146 0.5 0.5 NUM iajs-3911 225 147 10 10 NUM iajs-3911 225 148 5.55e-05 5.55e-05 NUM iajs-3911 225 149 0.010901 0.010901 NUM iajs-3911 225 150 5.55124e-05 5.55124e-05 NUM iajs-3911 225 151 0.75 0.75 NUM iajs-3911 225 152 0.5 0.5 NUM iajs-3911 225 153 20 20 NUM iajs-3911 225 154 1.69e-08 1.69e-08 NUM iajs-3911 225 155 8.48e-06 8.48e-06 NUM iajs-3911 225 156 1.69141e-08 1.69141e-08 NUM iajs-3911 225 157 0.75 0.75 NUM iajs-3911 225 158 0.5 0.5 NUM iajs-3911 225 159 30 30 NUM iajs-3911 225 160 2.77e-10 2.77e-10 NUM iajs-3911 225 161 1.64e-06 1.64e-06 NUM iajs-3911 225 162 2.77344e-10 2.77344e-10 NUM iajs-3911 225 163 0.75 0.75 NUM iajs-3911 225 164 0.5 0.5 NUM iajs-3911 225 165 50 50 NUM iajs-3911 225 166 1.12e-06 1.12e-06 NUM iajs-3911 225 167 0.003646 0.003646 NUM iajs-3911 225 168 1.12329e-06 1.12329e-06 NUM iajs-3911 225 169 0.75 0.75 NUM iajs-3911 225 170 1 1 NUM iajs-3911 225 171 10 10 NUM iajs-3911 225 172 1.16e-06 1.16e-06 NUM iajs-3911 225 173 0.006332 0.006332 NUM iajs-3911 225 174 1.16403e-06 1.16403e-06 NUM iajs-3911 225 175 0.75 0.75 NUM iajs-3911 225 176 1 1 NUM iajs-3911 225 177 20 20 NUM iajs-3911 225 178 2.29e-08 2.29e-08 NUM iajs-3911 225 179 4.14e-05 4.14e-05 NUM iajs-3911 225 180 2.29383e-08 2.29383e-08 NUM iajs-3911 225 181 0.75 0.75 NUM iajs-3911 225 182 1 1 NUM iajs-3911 225 183 30 30 NUM iajs-3911 225 184 3.09e-10 3.09e-10 NUM iajs-3911 225 185 0.001051 0.001051 NUM iajs-3911 225 186 3.09264e-10 3.09264e-10 NUM iajs-3911 225 187 0.75 0.75 NUM iajs-3911 225 188 1 1 NUM iajs-3911 225 189 50 50 NUM iajs-3911 225 190 4.93e-11 4.93e-11 NUM iajs-3911 225 191 0.002993 0.002993 NUM iajs-3911 225 192 4.92781e-11 4.92781e-11 NUM iajs-3911 225 193 0.75 0.75 NUM iajs-3911 225 194 1.5 1.5 NUM iajs-3911 225 195 10 10 NUM iajs-3911 225 196 1.98e-06 1.98e-06 NUM iajs-3911 225 197 0.000167 0.000167 NUM iajs-3911 225 198 1.98306e-06 1.98306e-06 NUM iajs-3911 225 199 0.75 0.75 NUM iajs-3911 225 200 1.5 1.5 NUM iajs-3911 225 201 20 20 NUM iajs-3911 225 202 3.31e-09 3.31e-09 NUM iajs-3911 225 203 0.0011 0.0011 NUM iajs-3911 225 204 3.31358e-09 3.31358e-09 NUM iajs-3911 225 205 0.75 0.75 NUM iajs-3911 225 206 1.5 1.5 NUM iajs-3911 225 207 30 30 NUM iajs-3911 225 208 2.99e-09 2.99e-09 NUM iajs-3911 225 209 1.7e-05 1.7e-05 NUM iajs-3911 225 210 2.98614e-09 2.98614e-09 NUM iajs-3911 225 211 0.75 0.75 NUM iajs-3911 225 212 1.5 1.5 NUM iajs-3911 225 213 50 50 NUM iajs-3911 225 214 9.37e-11 9.37e-11 NUM iajs-3911 225 215 0.000217 0.000217 NUM iajs-3911 225 216 9.37347e-11 9.37347e-11 NUM iajs-3911 225 217 5 5 NUM iajs-3911 225 218 . . PUNCT iajs-3911 225 219 conclusion conclusion NOUN iajs-3911 225 220 in in ADP iajs-3911 225 221 this this DET iajs-3911 225 222 paper paper NOUN iajs-3911 225 223 , , PUNCT iajs-3911 225 224 we we PRON iajs-3911 225 225 have have AUX iajs-3911 225 226 considered consider VERB iajs-3911 225 227 the the DET iajs-3911 225 228 bayesian bayesian NOUN iajs-3911 225 229 estimation estimation NOUN iajs-3911 225 230 of of ADP iajs-3911 225 231 the the DET iajs-3911 225 232 unknown unknown ADJ iajs-3911 225 233 parameters parameter NOUN iajs-3911 225 234 of of ADP iajs-3911 225 235 the the DET iajs-3911 225 236 two two NUM iajs-3911 225 237 - - PUNCT iajs-3911 225 238 parameter parameter NOUN iajs-3911 225 239 exponential exponential ADJ iajs-3911 225 240 - - PUNCT iajs-3911 225 241 rayleigh rayleigh NOUN iajs-3911 225 242 distribution distribution NOUN iajs-3911 225 243 . . PUNCT iajs-3911 226 1 simulation simulation NOUN iajs-3911 226 2 procedure procedure NOUN iajs-3911 226 3 using use VERB iajs-3911 226 4 montecarlo montecarlo NOUN iajs-3911 226 5 technique technique NOUN iajs-3911 226 6 and and CCONJ iajs-3911 226 7 through through ADP iajs-3911 226 8 previous previous ADJ iajs-3911 226 9 tables table NOUN iajs-3911 226 10 show show VERB iajs-3911 226 11 us we PRON iajs-3911 226 12 that that SCONJ iajs-3911 226 13 the the DET iajs-3911 226 14 estimated estimate VERB iajs-3911 226 15 values value NOUN iajs-3911 226 16 and and CCONJ iajs-3911 226 17 two two NUM iajs-3911 226 18 distribution distribution NOUN iajs-3911 226 19 parameters parameter NOUN iajs-3911 226 20 are be AUX iajs-3911 226 21 influenced influence VERB iajs-3911 226 22 by by ADP iajs-3911 226 23 both both DET iajs-3911 226 24 ( ( PUNCT iajs-3911 226 25 sample sample NOUN iajs-3911 226 26 size size NOUN iajs-3911 226 27 , , PUNCT iajs-3911 226 28 real real ADJ iajs-3911 226 29 value value NOUN iajs-3911 226 30 for for ADP iajs-3911 226 31 estimator estimator NOUN iajs-3911 226 32 and and CCONJ iajs-3911 226 33 estimation estimation NOUN iajs-3911 226 34 method method NOUN iajs-3911 226 35 ) ) PUNCT iajs-3911 226 36 , , PUNCT iajs-3911 226 37 we we PRON iajs-3911 226 38 find find VERB iajs-3911 226 39 that that SCONJ iajs-3911 226 40 the the DET iajs-3911 226 41 lindely lindely ADV iajs-3911 226 42 approximation approximation NOUN iajs-3911 226 43 estimation estimation NOUN iajs-3911 226 44 method method NOUN iajs-3911 226 45 is be AUX iajs-3911 226 46 the the DET iajs-3911 226 47 best good ADJ iajs-3911 226 48 for for ADP iajs-3911 226 49 the the DET iajs-3911 226 50 parameters parameter NOUN iajs-3911 226 51 ( ( PUNCT iajs-3911 226 52 Ξ± Ξ± NOUN iajs-3911 226 53 and and CCONJ iajs-3911 226 54 Ξ» Ξ» NOUN iajs-3911 226 55 ) ) PUNCT iajs-3911 226 56 . . PUNCT iajs-3911 227 1 bayes bayes PROPN iajs-3911 227 2 estimators estimator NOUN iajs-3911 227 3 were be AUX iajs-3911 227 4 obtained obtain VERB iajs-3911 227 5 using use VERB iajs-3911 227 6 lindley lindley NOUN iajs-3911 227 7 approximation approximation NOUN iajs-3911 227 8 and and CCONJ iajs-3911 227 9 tierney tierney PROPN iajs-3911 227 10 and and CCONJ iajs-3911 227 11 kadane kadane PROPN iajs-3911 227 12 approximation approximation NOUN iajs-3911 227 13 while while SCONJ iajs-3911 227 14 mle mle PROPN iajs-3911 227 15 were be AUX iajs-3911 227 16 obtained obtain VERB iajs-3911 227 17 using use VERB iajs-3911 227 18 newton newton PROPN iajs-3911 227 19 - - PUNCT iajs-3911 227 20 raphson raphson PROPN iajs-3911 227 21 method method NOUN iajs-3911 227 22 , , PUNCT iajs-3911 227 23 simulation simulation NOUN iajs-3911 227 24 study study NOUN iajs-3911 227 25 was be AUX iajs-3911 227 26 conducted conduct VERB iajs-3911 227 27 to to PART iajs-3911 227 28 examine examine VERB iajs-3911 227 29 and and CCONJ iajs-3911 227 30 compare compare VERB iajs-3911 227 31 the the DET iajs-3911 227 32 lindely lindely ADV iajs-3911 227 33 approximation approximation NOUN iajs-3911 227 34 estimation estimation NOUN iajs-3911 227 35 method method NOUN iajs-3911 227 36 with with ADP iajs-3911 227 37 tierney tierney PROPN iajs-3911 227 38 and and CCONJ iajs-3911 227 39 kadane kadane PROPN iajs-3911 227 40 approximation approximation NOUN iajs-3911 227 41 for for ADP iajs-3911 227 42 different different ADJ iajs-3911 227 43 sample sample NOUN iajs-3911 227 44 sizes size NOUN iajs-3911 227 45 with with ADP iajs-3911 227 46 different different ADJ iajs-3911 227 47 values value NOUN iajs-3911 227 48 showing show VERB iajs-3911 227 49 that that SCONJ iajs-3911 227 50 the the DET iajs-3911 227 51 lindely lindely ADV iajs-3911 227 52 approximation approximation NOUN iajs-3911 227 53 estimation estimation NOUN iajs-3911 227 54 method method NOUN iajs-3911 227 55 is be AUX iajs-3911 227 56 the the DET iajs-3911 227 57 best good ADJ iajs-3911 227 58 when when SCONJ iajs-3911 227 59 we we PRON iajs-3911 227 60 use use VERB iajs-3911 227 61 mean mean ADJ iajs-3911 227 62 squares square NOUN iajs-3911 227 63 error error NOUN iajs-3911 227 64 for for ADP iajs-3911 227 65 the the DET iajs-3911 227 66 parameter parameter NOUN iajs-3911 227 67 ( ( PUNCT iajs-3911 227 68 Ξ± Ξ± NOUN iajs-3911 227 69 and and CCONJ iajs-3911 227 70 Ξ» Ξ» NOUN iajs-3911 227 71 ) ) PUNCT iajs-3911 227 72 . . PUNCT iajs-3911 228 1 noting note VERB iajs-3911 228 2 that that SCONJ iajs-3911 228 3 the the DET iajs-3911 228 4 lindely lindely ADV iajs-3911 228 5 approximation approximation NOUN iajs-3911 228 6 estimation estimation NOUN iajs-3911 228 7 method method NOUN iajs-3911 228 8 is be AUX iajs-3911 228 9 the the DET iajs-3911 228 10 best good ADJ iajs-3911 228 11 when when SCONJ iajs-3911 228 12 we we PRON iajs-3911 228 13 use use VERB iajs-3911 228 14 mean mean VERB iajs-3911 228 15 squares square NOUN iajs-3911 228 16 error error NOUN iajs-3911 228 17 for for ADP iajs-3911 228 18 survival survival NOUN iajs-3911 228 19 function function NOUN iajs-3911 228 20 . . PUNCT iajs-3911 229 1 ihjpas ihjpas PROPN iajs-3911 229 2 . . PUNCT iajs-3911 230 1 2025,38(2 2025,38(2 PROPN iajs-3911 230 2 ) ) PUNCT iajs-3911 230 3 416 416 NUM iajs-3911 230 4 acknowledgment acknowledgment NOUN iajs-3911 230 5 the the DET iajs-3911 230 6 referees referee NOUN iajs-3911 230 7 ' ' PART iajs-3911 230 8 insightful insightful ADJ iajs-3911 230 9 feedback feedback NOUN iajs-3911 230 10 and and CCONJ iajs-3911 230 11 recommendations recommendation NOUN iajs-3911 230 12 for for ADP iajs-3911 230 13 enhancing enhance VERB iajs-3911 230 14 the the DET iajs-3911 230 15 work work NOUN iajs-3911 230 16 are be AUX iajs-3911 230 17 much much ADV iajs-3911 230 18 appreciated appreciated ADJ iajs-3911 230 19 by by ADP iajs-3911 230 20 the the DET iajs-3911 230 21 writers writer NOUN iajs-3911 230 22 . . PUNCT iajs-3911 231 1 conflict conflict NOUN iajs-3911 231 2 of of ADP iajs-3911 231 3 interest interest NOUN iajs-3911 231 4 the the DET iajs-3911 231 5 authors author NOUN iajs-3911 231 6 claim claim VERB iajs-3911 231 7 they they PRON iajs-3911 231 8 have have VERB iajs-3911 231 9 no no DET iajs-3911 231 10 rival rival ADJ iajs-3911 231 11 interests interest NOUN iajs-3911 231 12 . . PUNCT iajs-3911 232 1 funding funding NOUN iajs-3911 232 2 in in ADP iajs-3911 232 3 order order NOUN iajs-3911 232 4 to to PART iajs-3911 232 5 prepare prepare VERB iajs-3911 232 6 for for ADP iajs-3911 232 7 publication publication NOUN iajs-3911 232 8 , , PUNCT iajs-3911 232 9 there there PRON iajs-3911 232 10 is be VERB iajs-3911 232 11 no no DET iajs-3911 232 12 funding funding NOUN iajs-3911 232 13 help help NOUN iajs-3911 232 14 . . PUNCT iajs-3911 233 1 references reference NOUN iajs-3911 233 2 1 1 NUM iajs-3911 233 3 . . X iajs-3911 233 4 ramos ramos PROPN iajs-3911 233 5 pl pl PROPN iajs-3911 233 6 , , PUNCT iajs-3911 233 7 rodrigues rodrigues PROPN iajs-3911 233 8 fa fa PROPN iajs-3911 233 9 , , PUNCT iajs-3911 233 10 ramos ramos PROPN iajs-3911 233 11 e e PROPN iajs-3911 233 12 , , PUNCT iajs-3911 233 13 dey dey PROPN iajs-3911 233 14 dk dk PROPN iajs-3911 233 15 , , PUNCT iajs-3911 233 16 louzada louzada PROPN iajs-3911 233 17 f. f. PROPN iajs-3911 233 18 power power PROPN iajs-3911 233 19 laws law NOUN iajs-3911 233 20 distributions distribution NOUN iajs-3911 233 21 in in ADP iajs-3911 233 22 objective objective ADJ iajs-3911 233 23 priors prior NOUN iajs-3911 233 24 . . PUNCT iajs-3911 234 1 statistica statistica PROPN iajs-3911 234 2 sinica sinica PROPN iajs-3911 234 3 . . PUNCT iajs-3911 235 1 2023;33:1959 2023;33:1959 PROPN iajs-3911 235 2 - - SYM iajs-3911 235 3 1984 1984 NUM iajs-3911 235 4 . . PUNCT iajs-3911 236 1 https://doi.org/10.5705/ss.202020.0521 https://doi.org/10.5705/ss.202020.0521 NOUN iajs-3911 236 2 2 2 NUM iajs-3911 236 3 . . PUNCT iajs-3911 236 4 hussein hussein PROPN iajs-3911 236 5 lk lk PROPN iajs-3911 236 6 , , PUNCT iajs-3911 236 7 hussein hussein PROPN iajs-3911 236 8 ih ih PROPN iajs-3911 236 9 , , PUNCT iajs-3911 236 10 rasheed rasheed VERB iajs-3911 236 11 ha ha INTJ iajs-3911 236 12 . . PUNCT iajs-3911 237 1 an an DET iajs-3911 237 2 estimation estimation NOUN iajs-3911 237 3 of of ADP iajs-3911 237 4 survival survival NOUN iajs-3911 237 5 and and CCONJ iajs-3911 237 6 hazard hazard NOUN iajs-3911 237 7 rate rate NOUN iajs-3911 237 8 functions function NOUN iajs-3911 237 9 of of ADP iajs-3911 237 10 exponential exponential ADJ iajs-3911 237 11 rayleigh rayleigh NOUN iajs-3911 237 12 distribution distribution NOUN iajs-3911 237 13 . . PUNCT iajs-3911 238 1 ibn ibn PROPN iajs-3911 238 2 al al PROPN iajs-3911 238 3 - - PUNCT iajs-3911 238 4 haitham haitham PROPN iajs-3911 238 5 journal journal PROPN iajs-3911 238 6 for for ADP iajs-3911 238 7 pure pure ADJ iajs-3911 238 8 and and CCONJ iajs-3911 238 9 applied applied ADJ iajs-3911 238 10 sciences science NOUN iajs-3911 238 11 . . PUNCT iajs-3911 239 1 2021;34:93 2021;34:93 NUM iajs-3911 239 2 - - SYM iajs-3911 239 3 107 107 NUM iajs-3911 239 4 . . PUNCT iajs-3911 240 1 https://doi.org/10.30526/34.4.2706 https://doi.org/10.30526/34.4.2706 X iajs-3911 241 1 3 3 X iajs-3911 241 2 . . PUNCT iajs-3911 241 3 shatti shatti PROPN iajs-3911 241 4 rn rn PROPN iajs-3911 241 5 , , PUNCT iajs-3911 241 6 al al PROPN iajs-3911 241 7 - - PUNCT iajs-3911 241 8 kinani kinani PROPN iajs-3911 241 9 ih ih X iajs-3911 241 10 . . PUNCT iajs-3911 242 1 estimating estimate VERB iajs-3911 242 2 the the DET iajs-3911 242 3 parameters parameter NOUN iajs-3911 242 4 of of ADP iajs-3911 242 5 exponential exponential ADJ iajs-3911 242 6 - - PUNCT iajs-3911 242 7 rayleigh rayleigh NOUN iajs-3911 242 8 distribution distribution NOUN iajs-3911 242 9 under under ADP iajs-3911 242 10 type type NOUN iajs-3911 242 11 - - PUNCT iajs-3911 242 12 i i PRON iajs-3911 242 13 censored censored ADJ iajs-3911 242 14 data datum NOUN iajs-3911 242 15 . . PUNCT iajs-3911 243 1 baghdad baghdad PROPN iajs-3911 243 2 science science PROPN iajs-3911 243 3 journal journal PROPN iajs-3911 243 4 . . PUNCT iajs-3911 244 1 2024;21:146 2024;21:146 NUM iajs-3911 244 2 - - SYM iajs-3911 244 3 150 150 NUM iajs-3911 244 4 . . PUNCT iajs-3911 245 1 https://doi.org/10.21123/bsj.2023.79627 https://doi.org/10.21123/bsj.2023.79627 NOUN iajs-3911 245 2 4 4 NUM iajs-3911 245 3 . . PUNCT iajs-3911 246 1 isaac isaac PROPN iajs-3911 246 2 rs rs PROPN iajs-3911 246 3 , , PUNCT iajs-3911 246 4 mehta mehta PROPN iajs-3911 246 5 nb nb PROPN iajs-3911 246 6 . . PROPN iajs-3911 246 7 efficient efficient ADJ iajs-3911 246 8 computation computation NOUN iajs-3911 246 9 of of ADP iajs-3911 246 10 multivariate multivariate NOUN iajs-3911 246 11 rayleigh rayleigh PROPN iajs-3911 246 12 and and CCONJ iajs-3911 246 13 exponential exponential ADJ iajs-3911 246 14 distributions distribution NOUN iajs-3911 246 15 . . PUNCT iajs-3911 247 1 ieee ieee PROPN iajs-3911 247 2 wireless wireless PROPN iajs-3911 247 3 communications communication NOUN iajs-3911 247 4 letters letter NOUN iajs-3911 247 5 . . PUNCT iajs-3911 248 1 2019;8:456 2019;8:456 NOUN iajs-3911 248 2 - - SYM iajs-3911 248 3 459 459 NUM iajs-3911 248 4 . . PUNCT iajs-3911 249 1 https://doi.org/10.1109/lwc.2018.2875999 https://doi.org/10.1109/lwc.2018.2875999 PROPN iajs-3911 249 2 5 5 NUM iajs-3911 249 3 . . 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PUNCT iajs-3911 253 13 comparing compare VERB iajs-3911 253 14 weibull weibull PROPN iajs-3911 253 15 stress stress NOUN iajs-3911 253 16 - - PUNCT iajs-3911 253 17 strength strength NOUN iajs-3911 253 18 reliability reliability NOUN iajs-3911 253 19 bayesian bayesian NOUN iajs-3911 253 20 estimators estimator NOUN iajs-3911 253 21 for for ADP iajs-3911 253 22 singly singly ADV iajs-3911 253 23 type type NOUN iajs-3911 253 24 ii ii PROPN iajs-3911 253 25 censored censor VERB iajs-3911 253 26 data datum NOUN iajs-3911 253 27 under under ADP iajs-3911 253 28 different different ADJ iajs-3911 253 29 loss loss NOUN iajs-3911 253 30 functions function NOUN iajs-3911 253 31 . . PUNCT iajs-3911 254 1 baghdad baghdad PROPN iajs-3911 254 2 science science PROPN iajs-3911 254 3 journal journal PROPN iajs-3911 254 4 . . PUNCT iajs-3911 255 1 2021;18:306 2021;18:306 NOUN iajs-3911 255 2 - - SYM iajs-3911 255 3 314 314 NUM iajs-3911 255 4 . . PUNCT iajs-3911 256 1 https://doi.org/10.21123/bsj.2021.18.2.0306 https://doi.org/10.21123/bsj.2021.18.2.0306 NOUN iajs-3911 256 2 7 7 NUM iajs-3911 256 3 . . PUNCT iajs-3911 257 1 al al PROPN iajs-3911 257 2 - - PUNCT iajs-3911 257 3 baldawi baldawi NOUN iajs-3911 257 4 . . PUNCT iajs-3911 258 1 tasnim tasnim NOUN iajs-3911 258 2 h.k h.k PROPN iajs-3911 258 3 . . PROPN iajs-3911 258 4 comparison comparison NOUN iajs-3911 258 5 of of ADP iajs-3911 258 6 maximum maximum ADJ iajs-3911 258 7 likelihood likelihood NOUN iajs-3911 258 8 and and CCONJ iajs-3911 258 9 some some DET iajs-3911 258 10 bayes bayes NOUN iajs-3911 258 11 estimators estimator NOUN iajs-3911 258 12 for for ADP iajs-3911 258 13 maxwell maxwell NOUN iajs-3911 258 14 distribution distribution NOUN iajs-3911 258 15 based base VERB iajs-3911 258 16 on on ADP iajs-3911 258 17 non non ADJ iajs-3911 258 18 - - ADJ iajs-3911 258 19 informative informative ADJ iajs-3911 258 20 priors prior NOUN iajs-3911 258 21 . . 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