资源描述：
《bayesian estimation for inequality constrained analysis of variance》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、3BayesianEstimationforInequalityConstrainedAnalysisofVarianceIreneKlugkistandJorisMulderDepartmentofMethodologyandStatistics,UtrechtUniversity,P.O.Box80140,3508TCUtrecht,theNetherlandsi.klugkist@uu.nlandj.mulder3@uu.nl3.1AShortIntroductiontoBayesianStatisticsInChapter2,seve
2、ralexamplesofresearchquestionsintheanalysisofvari-ance(ANOVA)contextwerepresented.ThemodelparametersofanANOVAaretwoormorepopulationmeansandthecommonandunknownresidualvariance.Intheexamples,thehypothesesorresearchquestionsofinterestimposeinequalityconstraintsonthemeans.Forin
3、stance,forthefour-groupANOVAintheDissociativeIdentityDisorder(DID)datafromHuntjensetal.[10],thehypothesisµcon>µamn>{µpat,µsim}representsoneofthetheoriesoftheresearchers.Inthischapter,BayesianestimationoftheparametersofinequalityconstrainedANOVAmodelsisintroduced.IntheBayesi
4、anapproach,knowledgeaboutmodelparametersisrepre-sentedbyaprobabilitydistribution.TwoimportantingredientsofBayesiananalysesarethepriordistributionandtheposteriordistributionofthepa-rameters.Thepriorrepresentstheknowledge(oruncertainty)aboutmodelparametersbeforeobservingtheda
5、ta.Afterobservingdata,theinformationinthedataiscombinedwiththeinformationintheprior,leadingtothepos-terior.Statedotherwise,theposteriordistributionrepresentstheknowledgeaboutmodelparametersafterobservingthedata.InBayesiananalyses,theroleofpriordistributionsisapointofdiscus-
6、sion.Manypriorspecificationscanbemadeanddifferentpriordistributionsmayleadtodifferentconclusions.BeforemovingtotheinequalityconstrainedANOVAmodel,thebasicprinciplesofBayesiananalysesandtheroleofpriordistributionshereinwillbeexplainedbasedonasimple,one-parameterprob-lem.Theexam
7、pledealswithestimationofapopulationmeanµassumingthatthevarianceisknown.ElaborateintroductionsintoBayesianmethodologyareprovidedby,forinstance,[2,6,8,14].28Klugkist,MulderTable3.1.RecognitionscoresofDID-patientsPatients’scores0122223M=3.11333333SD=1.59444467N=193.1.1TheDataT
8、heexamplewillbeillustratedbypartoftheDIDdataintroducedinChapter2.Thefocusisonestim
