期刊
ANNALS OF STATISTICS
卷 38, 期 5, 页码 2587-2619出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/10-AOS792
关键词
Bayesian model selection; empirical Bayes; multiple testing; variable selection
资金
- U.S. National Science Foundation [AST-0507481, DMS-01-03265]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0757549] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0757527, 0757367] Funding Source: National Science Foundation
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.
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