Exact Bayes Factors for the Comparison of Multinomial Distributions

This article deals with the problem of comparing multinomial distributions with multiple ordered categories. A graphical procedure is proposed for obtaining the posterior probabilities for the hypotheses of a stochastic dominance relationship, positive cumulative odds ratios, and a likelihood ratio ordering. From these expressions we subsequently obtain exact expressions for the Bayes factors related to these hypotheses. Supplemental materials for running the analysis for the examples presented in the article are available online.