This article considers Bayesian inference about collections of unknown distributions subject to a partial stochastic ordering. To address problems in testing of equalities between groups and estimation of group-specific distributions, we propose classes of restricted dependent Dirichlet process priors. These priors have full support in the space of stochastically ordered distributions, and can be used for collections of unknown mixture distributions to obtain a flexible class of mixture models. Theoretical properties are discussed, efficient methods are developed for posterior computation using Markov chain Monte Carlo, and the methods are illustrated using data from a study of DNA damage and repair.
Keywords: Dependent Dirichlet process; Hypothesis testing; Mixture model; Nonparametric Bayes; Order restriction.