The Bayesian information criterion: Background, derivation, and applications

Abstract

The Bayesian information criterion (BIC) is one of the most widely known and pervasively used tools in statistical model selection. Its popularity is derived from its computational simplicity and effective performance in many modeling frameworks, including Bayesian applications where prior distributions may be elusive. The criterion was derived by Schwarz (Ann Stat 1978, 6:461-464) to serve as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. This article reviews the conceptual and theoretical foundations for BIC, and also discusses its properties and applications. © 2011 Wiley Periodicals, Inc.