Open Access
April 2005 Spike and slab variable selection: Frequentist and Bayesian strategies
Hemant Ishwaran, J. Sunil Rao
Ann. Statist. 33(2): 730-773 (April 2005). DOI: 10.1214/009053604000001147


Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation. Specifically, we study the usefulness of continuous bimodal priors to model hypervariance parameters, and the effect scaling has on the posterior mean through its relationship to penalization. Several model selection strategies, some frequentist and some Bayesian in nature, are developed and studied theoretically. We demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification, and show this is achieved using the posterior from a rescaled spike and slab model. We also show how to verify a procedure’s ability to reduce model uncertainty in finite samples using a specialized forward selection strategy. Using this tool, we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty.


Download Citation

Hemant Ishwaran. J. Sunil Rao. "Spike and slab variable selection: Frequentist and Bayesian strategies." Ann. Statist. 33 (2) 730 - 773, April 2005.


Published: April 2005
First available in Project Euclid: 26 May 2005

zbMATH: 1068.62079
MathSciNet: MR2163158
Digital Object Identifier: 10.1214/009053604000001147

Primary: 62J07
Secondary: 62J05

Keywords: Generalized ridge regression , hypervariance , model averaging , model uncertainty , ordinary least squares , Penalization , rescaling , shrinkage , stochastic variable selection , Zcut

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.33 • No. 2 • April 2005
Back to Top