Criteria for Bayesian Model Choice with Application to Variable Selection

• Activity Number: 506
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Jim Berger*+ and Susie Bayarri and Anabel Forte and Gonzalo Garcia-Donato
• Companies: Duke University and University of Valencia and Universitat Jaume I and Universidad de Castilla-La Mancha
• Keywords: Model selection ; Variable selection ; Objective Bayes

Abstract

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.