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Understanding predictive information criteria for Bayesian models . Andrew Gelman , Jessica Hwang , and Aki Vehtari . 14 Aug 2013. Abstract We review the Akaike, deviance, and Watanabe-Akaike information criteria from a Bayesian perspective, where the goal is to estimate expected out-of-sample-prediction error using a bias- corrected adjustment of within-sample error. We focus on the choices involved in setting up these measures, and we compare them in three simple examples, one theoretical and two applied. The contribution of this review is to put all these information criteria into a Bayesian predictive context and to better understand, through small examples, how these methods can apply in practice. Keywords: AIC, DIC, WAIC, cross-validation, prediction, Bayes 1. Introduction Bayesian models can be evaluated and compared in several ways. Most simply, any model or set of models can be taken as an exhaustive set, in which case all inference is summarized by the posterior distribution.
contribution of this review is to put all these information criteria into a Bayesian predictive context and to better understand, through small examples, how these methods can apply in practice. Keywords: AIC, DIC, WAIC, cross-validation, prediction, Bayes 1. Introduction Bayesian models can be evaluated and compared in several ways.
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