bayesian models for sparse regression analysis of high dimensional data

《bayesian models for sparse regression analysis of high dimensional data》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、BayesianModelsforSparseRegressionAnalysisofHighDimensionalData*UniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:9780199694587PublishedtoOxford

2、ScholarshipOnline:January2012DOI:10.1093/acprof:oso/9780199694587.001.0001BayesianModelsforSparseRegressionAnalysisofHighDimensionalData*SylviaRichardsonLeonardoBottoloJeffreyS.RosenthalDOI:10.1093/acprof:oso/9780199694587.003.0018AbstractandKeywordsThispaperconsidersthetaskofbuildingefficientregr

3、essionmodelsforsparsemultivariateanalysisofhighdimensionaldatasets,inparticularitfocusesoncaseswherethenumbersqofresponsesY=(yk,1≤k≤q)andpofpredictorsX=(xj,1≤j≤p)toanalysejointlyarebothlargewithrespecttothesamplesizen,achallengingbi‐directionaltask.Theanalysisofsuchdatasetsarisecommonlyingenetical

4、genomics,withXlinkedtotheDNAcharacteristicsandYcorrespondingtomeasurementsoffundamentalbiologicalprocessessuchastranscription,proteinormetaboliteproduction.BuildingontheBayesianvariableselectionset‐upforthelinearmodelandassociatedefficientMCMCalgorithmsdevelopedforsingleresponses,wediscussthegener

5、icframeworkofhierarchicalrelatedsparseregressions,whereparallelregressionsofykPage1of35BayesianModelsforSparseRegressionAnalysisofHighDimensionalData*onthesetofcovariatesXarelinkedinahierarchicalfashion,inparticularthroughthepriormodelofthevariableselectionindicatorsγkj,whichindicateamongthecovari

6、atesxjthosewhichareassociatedtotheresponseykineachmultivariateregression.Structuresforthejointmodeloftheγkj,whichcorrespondtodifferentcompromisesbetweentheaimsofcontrollingsparsityandthatofenhancingthedetectionofpredictorsthatareassociatedwithmanyresponses(“hotspots”),willbediscussedandanewmultipl

7、icativemodelfortheprobabilitystructureoftheγkjwillbepresented.Toperforminferenceforthesemodelsinhighdimensionalset‐ups,noveladaptiveMCMCalgorithmsareneeded.Assparsityisparamountandmostoftheassociationsexpectedtob