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1、MarkovChainMonteCarloMethodswithRHans-PeterHelfrichUniversityofBonnTheodor-Brinkmann-GraduateSchoolH.-P.Helfrich(UniversityofBonn)MCMCBrinkmannSchool1/21Overview1Introduction2Linearregression3Meta-analysis4ReferencesH.-P.Helfrich(UniversityofBonn)MCMCBr
2、inkmannSchool2/21IntroductionObjectivesInthislecture,IwanttoshowhowtodoBayesiandataanalysis.ThestartingpointisBayes'theoremwhichgivesposteriorprobabilitydistributionsfortheparameterstobeestimated.Onlyinafewcases,thedistributioncanbeanalyticallycalculate
3、d.ThestandardtoolsaretheMarkovChainMonteCarloMethodandGibbssamplingasaspecialcase.TheBUGSprojectTheBUGS(BayesianinferenceUsingGibbsSampling)projectisconcernedwith
exiblesoftwarefortheBayesiananalysisofcomplexstatisticalmodelsusingMarkovchainMonteCarlo(M
4、CMC)methods.Theprojectbeganin1989intheMRCBiostatisticsUnitandledinitiallytothe`Classic'BUGSprogram,andthenontotheWinBUGSsoftwaredevelopedjointlywiththeImperialCollegeSchoolofMedicineatStMary's,London.H.-P.Helfrich(UniversityofBonn)MCMCBrinkmannSchool3/2
5、1WinBUGSisastandaloneprogramfreelyavailableatTheBUGSproject.Itfeaturesagraphicaluserinterfaceandon-linemonitoringandconvergencediagnostics.H.-P.Helfrich(UniversityofBonn)MCMCBrinkmannSchool4/21UsingMarkovChainMonteCarlomethodsTheRBugspackage[Gelmanetal.
6、,2004]http://www.stat.columbia.edu/gelman/bugsR/software.pdfmaybeusedforcallingWinBUGSwithinR.AllnecessarystepscanbedoneinR.TheR2WinBUGSpackage[Sturtzetal.,2005]providesconvenientfunctionstocallWinBUGSortheopensourcecounterpartOpenBUGsfromRMATBUGShttp:/
7、/code.google.com/p/matbugs/givesaMatlabinterfaceforWinBUGS.WecanimplementtheMarkovChainMonteCarloMethodinR,Matlab,orsomeotherprogramminglanguageWemayuseapackagefromtheRlibraries,e.g.,MCMCpackhttp://adm.wustl.edu/media/pdfs/rnews06.pdfwhichimplementstheM
8、CMCmethodamongotherthingsH.-P.Helfrich(UniversityofBonn)MCMCBrinkmannSchool5/21LinearregressionModelWeconsiderthestandardlinearregressionprocessmodely=ax+bforgivendatax1;x2;:::;xNandy1;y2:::;yN.Forthedatamodel,weassumethatthey-va
