epsilon-Contaminated priors in contingency tables

Abstract

An r x s table is used for different approaches to statistical inference. We develop a Bayesian procedure to test simple null hypotheses versus bilateral alternatives in contingency tables. We consider testing equality of proportions of independent multinomial distributions when the common proportions are known. A lower bound of the posterior probabilities of the null hypothesis is calculated with respect to a mixture of a point prior on the null and an epsilon-contaminated prior on the proportions under the alternative. The resulting Bayes tests are compared numerically to Pearson's chi(2) in a number of examples. For the examined examples the lower bound and the p-value can be made close. The obtained results are generalized when the common proportions vector under the null is unknown or has a known functional form.