Spike and slab variable selection: Frequentist and Bayesian strategies

• 成果类型: Article
• 署名作者: Ishwaran, H; Rao, JS
• 署名单位: Cleveland Clinic Foundation; University System of Ohio; Case Western Reserve University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000001147
• 发表日期: 2005
• 页码: 730-773
• 关键词: least angle regression; linear-model selection; multiple shrinkage; Cross-validation; subset-selection; bootstrap; prediction; estimators

摘要

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.