Desiderata for Prior Distributions in Bayesian Model Selection

• Activity Number: 669
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Memorial
• Author(s): Merlise Clyde*
• Companies: Duke University
• Keywords: Model Selection ; Bayesian Model Averaging ; Robust Prior ; Gaussian Hypergeometric ; Bayes Factors

Abstract

Bayesian model comparison requires the specification of prior distributions for the parameters defined for each candidate model; in applications such as variable selection in linear models this task becomes quickly daunting as the number of models grows rapidly with the number of predictors. Because of the difficulty of subjective prior specification, there have been a number of attempts to define conventional or objective prior distributions for Bayesian model selection. While many have been shown to have desirable properties, there has been no uniform consensus as to which are the most successful. In 2012 Susie Bayarri and colleagues formalized the most general and compelling of the various criteria that had been deemed essential for model selection priors (such as consistency of the resulting procedure, invariance), with the goal of determining if these criteria can essentially determine objective priors. These criteria led Bayarri et al to propose a new model selection prior, the "robust prior", which is appealing for its theoretical and computational properties in linear models.