Bayesian inference and the parametric bootstrap Efron 2013 .pdf

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1、TheAnnalsofAppliedStatistics2012,Vol.6,No.4,1971–1997DOI:10.1214/12-AOAS571cInstituteofMathematicalStatistics,2012BAYESIANINFERENCEANDTHEPARAMETRICBOOTSTRAPByBradleyEfron1StanfordUniversityTheparametricbootstrapcanbeusedfortheefficientcomputa-tionofBayesposteriordistributions.Imp

2、ortancesamplingformulastakeonaneasyformrelatingtothedevianceinexponentialfami-liesandareparticularlysimplestartingfromJeffreysinvariantprior.Becauseofthei.i.d.natureofbootstrapsampling,familiarformulasdescribethecomputationalaccuracyoftheBayesestimates.Besidescomputationalmethod

3、s,thetheoryprovidesaconnectionbetweenBayesianandfrequentistanalysis.Efficientalgorithmsforthefre-quentistaccuracyofBayesianinferencesaredevelopedanddemon-stratedinamodelselectionexample.1.Introduction.Thisarticleconcernstheuseoftheparametricboot-straptocarryoutBayesianinferenceca

4、lculations.Twomainpointsaremade:thatinthecomparativelylimitedsetofcaseswherebootstrapmeth-odsapply,theyofferanefficientandcomputationallystraightforwardwaytocomputeposteriordistributionsandestimates,enjoyingsomeadvantagesoverMarkovchaintechniques;and,moreimportantly,thattheparamet

5、ricbootstraphelpsconnectBayesandfrequentistpointsofview.Thebasicideaissimpleandnotunfamiliar:thatthebootstrapisuse-fulforimportancesamplingcomputationofBayesposteriordistributions.AnimportantpaperbyNewtonandRaftery(1994)suggestedaversionofnonparametricbootstrappingforthispurpos

6、e.By“goingparametric”wecanmaketheBayes/bootstraprelationshipmoretransparent.ThislineofthoughthastheadvantageoflinkingratherthanseparatingfrequentistandBayesianpractices.arXiv:1301.2936v1[stat.AP]14Jan2013Section2introducesthemainideasintermsofanelementaryone-parame-terexamplean

7、dillustratesaconnectionbetweenJeffreysinvariantpriorden-sityandsecond-orderaccuratebootstrapconfidencelimits.BothmethodsReceivedMay2012;revisedMay2012.1SupportedinpartbyNIHGrant8R01EB002784andbyNSFGrantDMS-08-04324/12-08787.Keywordsandphrases.Jeffreysprior,exponentialfamilies,devi

8、ance,generalizedlin-earmodels.Thisisanelectronicreprin