Bayesian rv1ethods for Partial Stochastic Orderings

We discuss two methods of making nonparametric Bayesian inference on probability measures subject to a partial stochastic ordering. The first method involves a nonparametric prior for a measure on partially ordered latent observations, the second involves rejection sampling. Computational approaches are discussed for each method, and interpretations of prior and posterior information are discussed. An application is presented in which inference is made on the number of independently segregating quantitative trait loci present in an animal population. Some key words: Dirichlet process prior; Latent variable model; Mixture model; Nonparametric Bayes; Quantitative trait loci.