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1、TheAnnalsofAppliedStatistics2012,Vol.6,No.4,1971–1997DOI:10.1214/12-AOAS571cInstituteofMathematicalStatistics,2012BAYESIANINFERENCEANDTHEPARAMETRICBOOTSTRAPByBradleyEfron1StanfordUniversityTheparametricbootstrapcanbeusedforthee?cientcomputa-tionofBayesposteriordistributions.Imp
2、ortancesamplingformulastakeonaneasyformrelatingtothedevianceinexponentialfami-liesandareparticularlysimplestartingfromJe?reysinvariantprior.Becauseofthei.i.d.natureofbootstrapsampling,familiarformulasdescribethecomputationalaccuracyoftheBayesestimates.Besidescomputationalmethod
3、s,thetheoryprovidesaconnectionbetweenBayesianandfrequentistanalysis.E?cientalgorithmsforthefre-quentistaccuracyofBayesianinferencesaredevelopedanddemon-stratedinamodelselectionexample.1.Introduction.Thisarticleconcernstheuseoftheparametricboot-straptocarryoutBayesianinferenceca
4、lculations.Twomainpointsaremade:thatinthecomparativelylimitedsetofcaseswherebootstrapmeth-odsapply,theyo?erane?cientandcomputationallystraightforwardwaytocomputeposteriordistributionsandestimates,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、dillustratesaconnectionbetweenJe?reysinvariantpriorden-sityandsecond-orderaccuratebootstrapcon?dencelimits.BothmethodsReceivedMay2012;revisedMay2012.1SupportedinpartbyNIHGrant8R01EB002784andbyNSFGrantDMS-08-04324/12-08787.Keywordsandphrases.Je?reysprior,exponentialfamilies,devi
8、ance,generalizedlin-earmodels.Thisisanelectronicreprin
