Understanding predictive information criteria for Bayesian ...

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.

Much has been written on all these methods in both theory and practice, and we do not attempt anything like a comprehensive review (for that, see Vehtari and Ojanen, 2012). Our unique contribution here is to view all these methods from the standpoint of Bayesian practice, with the goal of understanding certain tools that are used to understand ...

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  Information, Methods, Understanding, Criteria, Predictive, Understanding predictive information criteria

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