  In social and biomedical sciences testing in contingency tables often
involves order restrictions on cell-probabilities parameters. We develop
objective Bayes methods for order-constrained testing and model comparison when
observations arise under product binomial or multinomial sampling.
Specifically, we consider tests for monotone order of the parameters against
equality of all parameters. Our strategy combines in a unified way both the
intrinsic prior methodology and the encompassing prior approach in order to
compute Bayes factors and posterior model probabilities. Performance of our
method is evaluated on several simulation studies and real datasets.
