Computing Bayesian predictive distributions: The K square and K prime distributions

Description

Niveau: Supérieur, Doctorat, Bac+8
ha l-0 01 13 70 5, v er sio n 1 - 1 4 N ov 2 00 6 Computing Bayesian predictive distributions: The K-square and K-prime distributions 14th November 2006 Jacques Poitevineau1, Bruno Lecoutre2 1ERIS and LAM/LCPE, UMR 7604, C.N.R.S., Universite Paris 6 et Ministere de la Culture, 11 rue de Lourmel, 75015 Paris, France. Email: 2ERIS, and Laboratoire de Mathematiques Raphael Salem, UMR 6085, C.N.R.S. et Universite de Rouen, Avenue de l'Universite, BP 12, 76801 Saint-Etienne-du-Rouvray, France. E-mail: Abstract The computation of two Bayesian predictive distributions which are discrete mixtures of incomplete beta functions is considered. The num- ber of iterations can easily become large for these distributions and thus, the accuracy of the result can be questionable. Therefore, existing algo- rithms for that class of mixtures are improved by introducing round-off error calculation into the stopping rule. A further simple modification is proposed to deal with possible underflows that may prevent recurrence to work properly. Keywords: Predictive distribution; Bayesian approach; Round-off error; Incomplete beta function 1 Introduction The K-square and K-prime distributions have been introduced in Lecoutre (1984).

• square distribu- tion


• bayesian approach


• gamma functions


• computing bayesian predictive


• prime distribution


• free- dom parameters


• alternate chi-square

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 9
• Langue: English

Extrait

ComputingBayesianpredictivedistributions: TheK-squareandK-primedistributions 14thNovember2006 JacquesPoitevineau 1 ,BrunoLecoutre 2 1 ERISandLAM/LCPE,UMR7604,C.N.R.S.,Universite´Paris6etMiniste`re delaCulture,11ruedeLourmel,75015Paris,France. Email:[e-mail] 2 ERIS,andLaboratoiredeMathe´matiquesRaphae¨lSalem, UMR6085,C.N.R.S.etUniversite´deRouen,Avenuedel’Universite´, BP12,76801Saint-Etienne-du-Rouvray,France. E-mail:[e-mail] Abstract ThecomputationoftwoBayesianpredictivedistributionswhichare discretemixturesofincompletebetafunctionsisconsidered.Thenum- berofiterationscaneasilybecomelargeforthesedistributionsandthus, theaccuracyoftheresultcanbequestionable.Therefore,existingalgo- rithmsforthatclassofmixturesareimprovedbyintroducinground-off errorcalculationintothestoppingrule.Afurthersimplemodificationis proposedtodealwithpossibleunderflowsthatmaypreventrecurrenceto workproperly. Keywords:Predictivedistribution;Bayesianapproach;Round-offerror;Incomplete betafunction 1Introduction TheK-squareandK-primedistributionshavebeenintroducedinLecoutre (1984).TheycanbecharacterizedasmixturesoftheclassicalnoncentralFand noncentraltdistributionsrespectively(Lecoutre,1999).Thesetwodistributions areinvolvedintheBayesianpredictiveapproachforplanningandmonitoring experiments(Lecoutre,2001).Inparticular,theyareusefultoolsforsample sizedetermination,usingthepredictivedistributionsoftheteststatisticsand ofthelimitsofconfidenceintervalsunderstandardnormalmodels,assuminga 1