The Annals of Statistics

Criteria for Bayesian model choice with application to variable selection

M. J. Bayarri, J. O. Berger, A. Forte, and G. García-Donato

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In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models. This results in a new model selection objective prior with a number of compelling properties.

Article information

Ann. Statist. Volume 40, Number 3 (2012), 1550-1577.

First available in Project Euclid: 5 September 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J05: Linear regression 62J15: Paired and multiple comparisons
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

Model selection variable selection objective Bayes


Bayarri, M. J.; Berger, J. O.; Forte, A.; García-Donato, G. Criteria for Bayesian model choice with application to variable selection. Ann. Statist. 40 (2012), no. 3, 1550--1577. doi:10.1214/12-AOS1013.

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