Abstract:
In comparing two or more populations, sometimes a model incorporating a certain probability order is desired. The Bayesian paradigm provides a convenient framework for the development of related modeling, since any probability order restriction imposed a priori on the population distributions is preserved to the posterior analysis. We present Bayesian nonparametric approaches to modeling and inference for distributions subject to probability order constraints. The focus will be on stochastic ordering, arguably, the most important probability order in applications. The nonparametric prior models are developed using Dirichlet process mixtures. Posterior inference is obtained through Markov chain Monte Carlo techniques. To illustrate the methodology, we consider an application to the analysis of serologic data from a continuous diagnostic measure for a particular disease (the data examples involve serology scores for Johne's disease in dairy cows). Here, stochastic ordering is incorporated, as a biologically plausible constraint, in the modeling for the distributions of serologic values for the diseased and non-diseased populations.