Journal
ANNALS OF STATISTICS
Volume 40, Issue 3, Pages 1550-1577Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/12-AOS1013
Keywords
Model selection; variable selection; objective Bayes
Categories
Funding
- Spanish Ministry of Education and Science [MTM2010-19528]
- NSF [DMS-06-35449, DMS-07-57549-001, DMS-10-07773]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1007773] Funding Source: National Science Foundation
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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.
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