Inference after checking multiple Bayesian models for data conflict and applications to mitigating the influence of rejected priors
The proposed procedure combines Bayesian model checking with robust Bayes acts to guide inference whether or not the model is found to be inadequate. 1. Check each model within a large class of models to determine which models conflict with the data and which are adequate. 2. For the set of adequate models, use entropy maximization, other distribution combination, or a robust-Bayes decision rule. This proposed procedure is illustrated by the application of a class of hierarchical models to a simple data set.
model checking imprecise probability model assessment model criticism prior-data conflict robust bayesian decision theory