bayesian variable selection for random intercept modeling of gaussian and non

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1、BayesianVariableSelectionforRandomInterceptModelingofGaussianandNon‐GaussianDataUniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:97801

2、99694587PublishedtoOxfordScholarshipOnline:January2012DOI:10.1093/acprof:oso/9780199694587.001.0001BayesianVariableSelectionforRandomInterceptModelingofGaussianandNon‐GaussianDataSylviaFrühwirth‐SchnatterHelgaWagnerDOI:10.1093/acprof:oso/9780199694587.003.0006AbstractandKeywordsThepaperdem

3、onstratesthatBayesianvariableselectionforrandominterceptmodelsiscloselyrelatedtotheappropriatechoiceofthedistributionofheterogeneity.If,forinstance,aLaplaceratherthananormalpriorisconsidered,weobtainaBayesianLassorandomeffectsmodelwhichallowsbothsmoothingand,additionally,individualshrinkag

4、eoftherandomeffectstoward0.Inaddition,westudyspike‐and‐slabrandomeffectsmodelswithbothanabsolutelycontinuousandaDiracspikeandprovidedetailsofMCMCestimationforallmodels.Simulationstudiescomparingthevariouspriorsshowthatthespike‐and‐slabrandomeffectsmodeloutperformsunimodal,non‐Gaussianprior

5、sasfarascorrectclassificationofnon‐zerorandomeffectsisconcernedandthatthereissurprisinglylittledifferencebetweenanabsolutelycontinuousandaDiracspike.ThePage1of43BayesianVariableSelectionforRandomInterceptModelingofGaussianandNon‐GaussianDatachoiceofappropriatecomponentdensities,however,isc

6、rucialandwewerenotabletoidentifyauniformlybestdistributionfamily.ThepaperconcludeswithanapplicationtoANOVAforbinomialdatausingalogitmodelwitharandomintercept.Keywords:BayesianLasso,MCMC,spike‐and‐slabpriors,shrinkageSummaryThepaperdemonstratesthatBayesianvariableselectionforrandomintercept

7、modelsiscloselyrelatedtotheappropriatechoiceofthedistributionofheterogeneity.If,forinstance,aLaplaceratherthananormalpriorisconsidered,weobtainaBayesianLassorandomeffectsmodelwhichallowsbothsmoothingand,additionally,individualshrinkageoftherandomeffectstoward0