Bayesian Methods for High Dimensional Linear Models

TitleBayesian Methods for High Dimensional Linear Models
Publication TypeBook Chapter
Year of Publication2013
AuthorsMallick H, Yi N
Book TitleJ Biom Biostat
Volume1
Pagination005
ISBN2155-6180
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.

DOI10.4172/2155-6180.S1-005
AbbreviationJ Biom Biostat
PubMed ID24511433
PubMed Central IDPMC3914549
Grant ListR01 GM069430 / GM / NIGMS NIH HHS / United States
U01 NS041588 / NS / NINDS NIH HHS / United States