A survey of Bayesian predictive methods for model assessment, selection and comparison

To date, several methods exist in the statistical literature formodel assessment, which purport themselves specifically as Bayesian predictive methods. The decision theoretic assumptions on which these methodsare based are not always clearly stated in the original articles, however.The aim of this survey is to provide a unified review of Bayesian predictivemodel assessment and selection methods, and of methods closely related tothem. We review the various assumptions that are made in this context anddiscuss the connections between different approaches, with an emphasis onhow each method approximates the expected utility of using a Bayesianmodel for the purpose of predicting future data.