Bayesian nonparametric inference on stochastic ordering

This article considers Bayesian inference on 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 (rDDP) priors. These rDDP 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 rDDP mixture models. Theoretical properties are discussed, efficient methods are developed for posterior computation using MCMC, and the methods are illustrated using data from a study of DNA damage and repair.