Bayesian Analysis of Stochastically Ordered Distributions of Categorical Variables

This paper considers a nite set of discrete distributions all having the same nite support. The problem of interest is to assess the strength of evidence produced by sampled data for a hypothesis of a speciied stochastic ordering among the underlying distributions and to estimate these distributions subject to the ordering. We present a Bayesian approach alternative to the use of the posterior probability of the hypothesis and the Bayes factor in favour of the hypothesis. Computational methods are developed for the implementation of Bayesian analyses. Examples are analyzed to illustrate the inferential and computational developments in the paper. The methodology employed for testing a hypothesis is seen to apply to a wide class of problems in Bayesian inference and has some distinct advantages.