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Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

dc.contributor.author Berger, JO
dc.contributor.author Scott, James G
dc.date.accessioned 2011-06-21T17:30:35Z
dc.date.issued 2010-10-01
dc.identifier.issn 0090-5364
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. © Institute of Mathematical Statistics, 2010.
dc.language.iso en_US
dc.relation.ispartof Annals of Statistics
dc.relation.isversionof 10.1214/10-AOS792
dc.title Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem
dc.title.alternative
dc.type Journal article
dc.description.version Version of Record
duke.date.pubdate 2010-10-0
duke.description.issue 5
duke.description.volume 38
dc.relation.journal Annals of Statistics
pubs.begin-page 2587
pubs.end-page 2619
pubs.issue 5
pubs.organisational-group Duke
pubs.organisational-group Statistical Science
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 38


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