BAYES AND EMPIRICAL-BAYES MULTIPLICITY ADJUSTMENT IN THE VARIABLE-SELECTION PROBLEM

• 成果类型: Article
• 署名作者: Scott, James G.; Berger, James O.
• 署名单位: University of Texas System; University of Texas Austin; Duke University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS792
• 发表日期: 2010
• 页码: 2587-2619
• 关键词: model; GROWTH

摘要

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains.