  Hierarchical models are increasingly used in many applications. Along with
this increased use comes a desire to investigate whether the model is
compatible with the observed data. Bayesian methods are well suited to
eliminate the many (nuisance) parameters in these complicated models; in this
paper we investigate Bayesian methods for model checking. Since we contemplate
model checking as a preliminary, exploratory analysis, we concentrate on
objective Bayesian methods in which careful specification of an informative
prior distribution is avoided. Numerous examples are given and different
proposals are investigated and critically compared.
