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# Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem

## DukeSpace

 dc.contributor.author Berger, James en_US dc.date.accessioned 2011-06-21T17:30:35Z dc.date.available 2011-06-21T17:30:35Z dc.date.issued 2010 en_US dc.identifier.citation Scott,James G.;Berger,James O.. 2010. Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem. Annals of Statistics 38(5): 2587-2619. en_US dc.identifier.issn 0090-5364 en_US dc.identifier.uri http://hdl.handle.net/10161/4408 dc.description.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. en_US dc.language.iso en_US en_US dc.publisher INST MATHEMATICAL STATISTICS en_US dc.relation.isversionof doi:10.1214/10-AOS792 en_US dc.subject bayesian model selection en_US dc.subject empirical bayes en_US dc.subject multiple testing en_US dc.subject variable selection en_US dc.subject gaussian graphical models en_US dc.subject growth en_US dc.subject priors en_US dc.subject statistics & probability en_US dc.title Bayes and Empirical-Bayes Multiplicity Adjustment in the Variable-Selection Problem en_US dc.title.alternative en_US dc.description.version Version of Record en_US duke.date.pubdate 2010-10-0 en_US duke.description.endpage 2619 en_US duke.description.issue 5 en_US duke.description.startpage 2587 en_US duke.description.volume 38 en_US dc.relation.journal Annals of Statistics en_US