Bayesian Methods for High Dimensional Linear ModelsHimel Mallick and Nengjun Yi*
Department of Biostatistics, University of Alabama at Birmingham, Birmingham, AL, USA
- *Corresponding Author:
- Nengjun Yi
Department of Biostatistics
Ryals Public Health Building 317F
University of Alabama at Birmingham
Birmingham, AL 35294, USA
Tel: (205) 934-4924
Fax: (205) 975-2540
E-mail: [email protected]
Received date: April 14, 2013; Accepted date: May 28, 2013; Published date: June 01, 2013
Citation: Mallick H, Yi N (2013) Bayesian Methods for High Dimensional Linear Models. J Biomet Biostat S1:005. doi: 10.4172/2155-6180.S1-005
Copyright: © 2013 Mallick H, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.