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1、MomentPriorsforBayesianModelChoicewithApplicationstoDirectedAcyclicGraphs*UniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:9780199694587Publ
2、ishedtoOxfordScholarshipOnline:January2012DOI:10.1093/acprof:oso/9780199694587.001.0001MomentPriorsforBayesianModelChoicewithApplicationstoDirectedAcyclicGraphs*GuidoConsonniLucaLaRoccaDOI:10.1093/acprof:oso/9780199694587.003.0004AbstractandKeywordsWeproposeanewmethodfortheobjectivecomparisonoft
3、wonestedmodelsbasedonnon‐localpriors.Morespecifically,startingwithadefaultpriorundereachofthetwomodels,weconstructamomentpriorunderthelargermodel,andthenusethefractionalBayesfactorforacomparison.Non‐localpriorshavebeenrecentlyintroducedtoobtainabetterseparationbetweennestedmodels,thusacceleratin
4、gthelearningbehaviour,relativetocurrentlyusedlocalpriors,whenthesmallermodelholds.Althoughtheargumentshowingthesuperiorperformanceofnon‐localpriorsisasymptotic,theimprovementtheyproduceisalreadyapparentforsmalltomoderatesamplessizes,whichmakesthemausefulandpracticaltool.Asaby‐product,itturnsoutt
5、hatroutinelyusedobjectivemethods,suchasordinaryfractionalBayesfactors,arealarminglyslowinPage1of31MomentPriorsforBayesianModelChoicewithApplicationstoDirectedAcyclicGraphs*learningthatthesmallermodelholds.Onthedownside,whenthelargermodelholds,non‐localpriorsexhibitaweakerdiscriminatorypoweragain
6、stsamplingdistributionsclosetothesmallermodel.However,thisdrawbackbecomesrapidlynegligibleasthesamplesizegrows,becausethelearningrateoftheBayesfactorunderthelargermodelisexponentiallyfast,whetheroneuseslocalornon‐localpriors.WeapplyourmethodologytodirectedacyclicgraphmodelshavingaGaussiandistrib
7、ution.Becauseoftherecursivenatureofthejointdensity,andtheassumptionofglobalparameterindependenceembodiedinourprior,calculationsneedonlybeperformedforindividualverticesadmittingadistinctparentstructureunderthetwographs;additi
