Bayesian variable selection via a benchmark in normal linear models  

作　　者：Jun Shao Kam-Wah Tsui Sheng Zhang 

机构地区：[1]KLATASDS-MOE,School of Statistics,East China Normal University Shanghai,People’s Republic of China [2]Department of Statistics,University ofWisconsin-Madison,Madison,WI,USA

出　　处：《Statistical Theory and Related Fields》2021年第1期70-81,共12页统计理论及其应用（英文）

基　　金：supported by the National Natural Science Foundation of China[grant number 11831008];the U.S.National Science Foundation[grant numbers DMS-1612873 and DMS-1914411].

摘　　要：With increasing appearances of high-dimensional data over the past two decades,variable selections through frequentist likelihood penalisation approaches and their Bayesian counterparts becomes a popular yet challenging research area in statistics.Under a normal linear model with shrinkage priors,we propose a benchmark variable approach for Bayesian variable selection.The benchmark variable serves as a standard and helps us to assess and rank the importance of each covariate based on the posterior distribution of the corresponding regression coefficient.For a sparse Bayesian analysis,we use the benchmark in conjunction with a modified BIC.We also develop our benchmark approach to accommodate models with covariates exhibiting group structures.Two simulation studies are carried out to assess and compare the performances amongthe proposed approach and other methods.Three real datasets are also analysed by using these methods for illustration.

关 键 词：BENCHMARK lasso sparse Bayes shrinkage prior 

分 类 号：O21[理学—概率论与数理统计]