title: Bayesian Methods for High Dimensional Linear Models.
abstract: In this article, we present a selective overview of some recent developments in Bayesian model and variable selection methods for high dimensional linear models. While most of the reviews in literature are based on conventional methods, we focus on recently developed methods, which have proven to be successful in dealing with high dimensional variable selection. First, we give a brief overview of the traditional model selection methods (viz. Mallow's Cp, AIC, BIC, DIC), followed by a discussion on some recently developed methods (viz. EBIC, regularization), which have occupied the minds of many statisticians. Then, we review high dimensional Bayesian methods with a particular emphasis on Bayesian regularization methods, which have been used extensively in recent years. We conclude by briefly addressing the asymptotic behaviors of Bayesian variable selection methods for high dimensional linear models under different regularity conditions.
authors: Department of Biostatistics, University of Alabama at Birmingham, Birmingham, AL, USA.
authors: Himel
authors: H
authors: Mallick
authors: Department of Biostatistics, University of Alabama at Birmingham, Birmingham, AL, USA.
authors: Nengjun
authors: N
authors: Yi
keywords: Bayesian hierarchical models; Bayesian model selection; Bayesian subset regression; Bayesian variable selection; High dimensional linear models; MCMC; Nonlocal priors; Penalized regression; Posterior consistency; Regularization; Shrinkage methods