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October 2010 Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
James G. Scott, James O. Berger
Ann. Statist. 38(5): 2587-2619 (October 2010). DOI: 10.1214/10-AOS792

Abstract

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.

Citation

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James G. Scott. James O. Berger. "Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem." Ann. Statist. 38 (5) 2587 - 2619, October 2010. https://doi.org/10.1214/10-AOS792

Information

Published: October 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1200.62020
MathSciNet: MR2722450
Digital Object Identifier: 10.1214/10-AOS792

Subjects:
Primary: 62J05, 62J15

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 5 • October 2010
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