Bayesian testing and estimation of association in a two-way contingency table

In a two-way contingency table, one is interested in checking the goodness of fit of simple models such as independence, quasi-independence, symmetry, and constant association, and estimating parameters that describe the association structure of the table. In a large table, one may be interested in detecting a few outlying cells that deviate from the main association pattern in the table. Bayesian tests of these hypotheses are described using a prior defined on the set of interaction terms of the log-linear model. These tests and associated estimation procedures have several advantages over classical fitting/estimation procedures. First, the tests can give measures of evidence in support of simple hypotheses. Second, the Bayes factors can be used to give estimates of association parameters of the table that allow for uncertainty that the hypothesized model is true. These methods are illustrated for a number of tables.