Comment: Bayesian Checking of the Second Levels of Hierarchical Models

Gelman, Andrew E.

Bayarri and Castellanos (BC) have written an interesting paper discussing two forms of posterior model check, one based on cross-validation and one based on replication of new groups in a hierarchical model. We think both these checks are good ideas and can become even more effective when understood in the context of posterior predictive checking. For the purpose of discussion, however, it is most interesting to focus on the areas where we disagree with BC.


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March 17, 2010