Bayesian Model Assessment and Selection Using Bregman Divergence

One of the fundamental steps in statistical modeling is to select the best-fitting model from a set of candidate models for given data. 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 that significantly 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.