Bayesian Comparison of Two Ordered Multinomial Populations
Herbert I. Weisberg · Biometrics · 1972
A Bayesian approach to the problem of comparing two multinomial distributions with k categories and a natural ordering of the categories is developed. Assuming independent Dirichlet priors, we obtain a convenient algorithm for computing the posterior probability that one distribution is stochastically larger than the other. The important special case k = 2 reduces to computing the posterior probability that one binomial proportion exceeds another. We consider the more general problem of finding the posterior distribution of the ratio of two such proportions.