Recently,variableselectionbasedonpenalizedregressionmethodshasreceivedagreatdealofattention,mostlythroughfrequentist'smodels.ThispaperinvestigatesregularizationregressionfromBayesianperspective.OurnewmethodextendstheBayesianLassoregression(ParkandCasella,2008)throughreplacingtheleastsquarelossandLassopenaltybycompositequantilelossfunctionandadaptiveLassopenalty,whichallowsdifferentpenalizationparametersfordifferentregressioncoefficients.BasedontheBayesianhierarchicalmodelframework,anefficientGibbssamplerisderivedtosimulatetheparametersfromposteriordistributions.Furthermore,westudytheBayesiancompositequantileregressionwithadaptivegroupLassopenalty.Thedistinguishingcharacteristicofthenewlyproposedmethodiscompletelydataadaptivewithoutrequiringpriorknowledgeoftheerrordistribution.Extensivesimulationsandtworealdataexamplesareusedtoexaminethegoodperformanceoftheproposedmethod.Allresultsconfirmthatournovelmethodhasbothrobustnessandhighefficiencyandoftenoutperformsotherapproaches.
