Hierarchical Bayesian Model for Contingency Tables

A hierarchical Bayes model for analysis of contingency tables is presented and, using it, inference about correlation parameter, logarithm of the odds ratio, is studied. For drawing random sample from the distribution of logarithm of the odds ratio, computational method of Gibbs sampling is used. For testing independence the use of the hierarchical Bayes in calculating the Bayes factor is introduced and in an applied example is employed.