The Robustness of a Hierarchical Model for Multinomials and Contingency Tables

Publisher Summary This chapter focuses on the robustness of a hierarchical model for multinomial and contingency tables. Hierarchical Bayesian models can be used in a completely Bayesian manner or in a manner that has been called semi-, or pseudo-, or quasi Bayesian. In the latter case, the hyperparameters, or possibly the hyperhyperparameters, etc., are estimated by non-Bayesian methods, or at least by some not purely Bayesian method such as by maximum likelihood. In the so-called non-Bayesian statistics, the use of the Ockham-Duns razor is sometimes called the principle of parsimony, and it encourages one to avoid having more parameters than are necessary. In hierarchical Bayesian methods, one similarly uses a principle of parsimony or hyper-razor. There are at least two different ways to test a model. One is by means of significance tests after observations are made. Another is by examining the robustness of a model, that is, by seeing if small changes in the model lead to small changes in the implications. Tests for robustness can sometimes be carried out by the device of imaginary results before making observations. When calculating a Bayes factor F1, reasonable robustness with respect to the choice of hyperhyperparameters has also been found.