Markov Chain Monte Carlo Methods with R.pdf

《Markov Chain Monte Carlo Methods with R.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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