Comment: Bayesian Checking of the Second Level of Hierarchical Models: Cross-Validated Posterior Predictive Checks Using Discrepancy Measures

摘要

We compliment Bayard and Castellanos (BC) on producing an interesting and insightful paper on model checking applied to the second level of hierarchical models. Distributions of test statistics (functions of the observed data not involving parameters) for judging appropriateness of hierarchical models typically involve nuisance (i.e., unknown) parameters. BC (2007) focus on ways to remove the dependency on nuisance parameters so that test statistics can be used to assess models, either through p-values or Berger's relative predictive surprise (RPS). They demonstrate shortcomings in terms of very low power of posterior predictive checks and a posterior empirical Bayesian method. They also demonstrate better performance of their partial posterior predictive (ppp) method over a prior empirical Bayesian method. Methods of Dey et al. (1998), O'Hagan (2003) and Marshall and Spiegel-halter (2003) also are compared.