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1、NonparametricBayesianNetworks*UniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:9780199694587PublishedtoOxfordScholarshipOnline:Janua
2、ry2012DOI:10.1093/acprof:oso/9780199694587.001.0001NonparametricBayesianNetworks*KatjaIckstadtBj?ornBornkampMarcoGrzegorczykJakobWieczorekMalikR.SheriffHernáanE.GreccoEliZamirDOI:10.1093/acprof:oso/9780199694587.003.0010AbstractandKeywordsAconvenientwayofmodellingcomplexinteractionsisbye
3、mployinggraphsornetworkswhichcorrespondtoconditionalindependencestructuresinanunderlyingstatisticalmodel.OnemainclassofmodelsinthisregardareBayesiannetworks,whichhavethedrawbackofmakingparametricassumptions.Bayesiannonparametricmixturemodelsofferapossibilitytoovercomethislimitation,butha
4、vehardlybeenusedincombinationwithnetworks.ThismanuscriptbridgesthisgapbyintroducingnonparametricBayesianPage1of40NonparametricBayesianNetworks*networkmodels.Wereview(parametric)Bayesiannetworks,inparticularGaussianBayesiannetworks,fromaBayesianperspectiveaswellasnonparametricBayesianmixt
5、uremodels.AfterwardsthesetwomodellingapproachesarecombinedintononparametricBayesiannetworks.ThenewmodelsarecomparedbothtoGaussianBayesiannetworksandtomixturemodelsinasimulationstudy,whereitturnsoutthatthenonparametricnetworkmodelsperformfavourablyinnon‐Gaussiansituations.Thenewmodelsarea
6、lsoappliedtoanexamplefromsystemsbiology,namelyfindingmoduleswithintheMAPKcascade.Keywords:GaussianBayesiannetworks,SystemsBiology,NonparametricMixtureModels,SpeciesSamplingModelsSummaryAconvenientwayofmodellingcomplexinteractionsisbyemployinggraphsornetworkswhichcorrespondtoconditionalin
7、dependencestructuresinanunderlyingstatisticalmodel.OnemainclassofmodelsinthisregardareBayesiannetworks,whichhavethedrawbackofmakingparametricassumptions.Bayesiannonparametricmixturemodelsofferapossibilitytoovercomethislimitation,buthavehardlybeenusedincombinationwithnetwo
