Bayesian Model Assessment and Selection Using Bregman Divergence

• Activity Number: 327 - Bayesian Model Selection
• Type: Topic Contributed
• Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Dipak K Dey* and Gyuhyeong Goh
• Companies: university of connecticut and Kansas State University
• Keywords: Bayesian model averaging, ; Bayesian model selection, ; Bregman divergence ; Predictive density

Abstract

Techniques in Bayesian model selection and assessment procedures have mostly been based on the predictive densities. In this paper, based on Bayesian decision theory, we introduce a new model selection criterion, called Bregman Divergence Criterion (BDC). The proposed criterion improves many existing Bayesian model selection methods such as Bayes factor, intrinsic Bayes factor, pseudo-Bayes factor, etc. In addition, using a Monte Carlo approach, we develop an efficient estimator which signicantly eases the computational burden associated with our approach and prove its consistency. The versatility of our methodology is demonstrated on both simulated and real data; to this end, some illustrative examples are provided for linear regression models and longitudinal data models.