Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models

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Probit and Logit Model Selection (2010, methodology): “In addition to the criteria so far used in the literature, we adopt Ando's ( 2007 ) predictive deviance information criterion (PDIC).”
An introduction to good practices in cognitive modeling (2015, methodology): “When estimation is achieved by posterior sampling, DIC [57], or its bias-corrected variant BPIC [58], are easy-tocompute alternatives.”
A survey of Bayesian predictive methods for model assessment, selection and comparison (2012, methodology): “Other information criteria are asymptotically equivalent to different forms of leave-one-out cross-validation, but it is not clear what relationship the criterion of Ando and Tsay (2010) has to cross-validation, since it is not possible to leave n data points out in the cross-validation approach.”