A Bayesian Information Criterion for Singular Models

• Activity Number: 665
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Host Chapter-Montreal
• Author(s): Mathias Drton*+ and Martyn Plummer
• Companies: University of Washington and International Agency for Research on Cancer
• Keywords: information criteria ; mixture model ; model selection ; reduced-rank regression

Abstract

Determining the number of components in mixture models or the rank in reduced-rank regression are two examples of model selection problems that involve singular models, meaning models whose Fisher-information matrices may fail to be invertible. Singular models do not obey the regularity conditions underlying the derivation of the classical Bayesian information criterion (BIC) whose penalty structure does not reflect the frequentist large-sample behavior of their marginal likelihood. While large-sample theory for the marginal likelihood of singular models has been developed recently, the resulting approximations depend on the true parameter value and lead to a paradox of circular reasoning. I will discuss a resolution to this problem and give a practical extension of the BIC to singular models.