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1、IntegratedObjectiveBayesianEstimationandHypothesisTestingUniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:9780199694587Publishe
2、dtoOxfordScholarshipOnline:January2012DOI:10.1093/acprof:oso/9780199694587.001.0001IntegratedObjectiveBayesianEstimationandHypothesisTestingJoséM.BernardoDOI:10.1093/acprof:oso/9780199694587.003.0001AbstractandKeywordsThecompletefinalproductofBayesianinferenceistheposteriordistribut
3、ionofthequantityofinterest.Importantinferencesummariesincludepointestimation,regionestimationandprecisehypothesestesting.Thosesummariesmayappropriatelybedescribedasthesolutiontospecificdecisionproblemswhichdependontheparticularlossfunctionchosen.Theuseofacontinuouslossfunctionleadst
4、oanintegratedsetofsolutionswherethesamepriordistributionmaybeusedthroughout.ObjectiveBayesianmethodsarethosewhichuseapriordistributionwhichonlydependsontheassumedmodelandthequantityofinterest.Asaconsequence,objectiveBayesianmethodsproduceresultswhichonlydependontheassumedmodelandthe
5、dataobtained.Thecombineduseofintrinsicdiscrepancy,aninvariantinformation‐basedlossfunction,andappropriatelydefinedreferencepriors,providesanintegratedobjectiveBayesiansolutiontobothestimationandhypothesistestingproblems.TheideasareillustratedwithPage1of82IntegratedObjectiveBayesianE
6、stimationandHypothesisTestingalargecollectionofnon‐trivialexamples.Keywords:Foundations,DecisionTheory,Kullback–LeiblerDivergence,IntrinsicDiscrepancy,ReferenceAnalysis,ReferencePriors,PointEstimation,IntervalEstimation,RegionEstimation,PreciseHypothesisTesting,Hardy–WeinbergEquilib
7、rium,ContingencyTablesSummaryThecompletefinalproductofBayesianinferenceistheposteriordistributionofthequantityofinterest.Importantinferencesummariesincludepointestimation,regionestimationandprecisehypothesestesting.Thosesummariesmayappropriatelybedescribedasthesolutiontospecificdeci
8、sionproblemswhichde
