BAYESIAN-ANALYSIS OF STOCHASTICALLY ORDERED DISTRIBUTIONS OF CATEGORICAL VARIABLES

This article considers a finite set of discrete distributions all havi ng the same finite support. The problem of interest is to assess the s trength of evidence produced by sampled data for a hypothesis of a spe cified stochastic ordering among the underlying distributions and to e stimate these distributions subject to the ordering. We present a Baye sian approach that is an alternative to using the posterior probabilit y of the hypothesis and the Bayes factor in favor of the hypothesis. W e develop computational methods for the implementation of Bayesian ana lyses. We analyze examples to illustrate inferential and computational developments. The methodology used for testing a hypothesis is seen t o apply to a wide class of problems in Bayesian inference and has some distinct advantages.