Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
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. © Institute of Mathematical Statistics, 2010.
Type
Journal articlePermalink
https://hdl.handle.net/10161/4408Published Version (Please cite this version)
10.1214/10-AOS792Publication Info
Scott, JG; & Berger, JO (2010). Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem.
Annals of Statistics, 38(5). pp. 2587-2619. 10.1214/10-AOS792. Retrieved from https://hdl.handle.net/10161/4408.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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James O. Berger
Arts and Sciences Distinguished Professor Emeritus of Statistics

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