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Criteria for Bayesian model choice with application to variable selection. (English) Zbl 1257.62023

Summary: 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.

MSC:

62F15 Bayesian inference
62J05 Linear regression; mixed models
62H99 Multivariate analysis
62C10 Bayesian problems; characterization of Bayes procedures
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