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The Dirichlet process (DP) is one of the most popular Bayesian nonparametricmodels. An open problem with the DP is how to choose its infinite dimensionalparameter (base measure) in case of lack of prior information. In this work wepresent the Imprecise DP (IDP) -- a prior near-ignorance DP-based model thatdoes not require any choice of this probability measure. It consists of a classof DPs obtained by letting the normalized base measure of the DP vary in theset of all probability measures. We discuss the tight connections of thisapproach with Bayesian robustness and in particular prior near-ignorancemodeling via sets of probabilities. We use this model to perform a Bayesianhypothesis test on the probability P(X<Y). We study the theoretical propertiesof the IDP test (e.g., asymptotic consistency), and compare it with thefrequentist Mann-Whitney-Wilcoxon rank test that is commonly employed as a teston P(X< Y). In particular we will show that our method is more robust, in thesense that it is able to isolate instances in which the aforementioned test isvirtually guessing at random.

Imprecise Dirichlet Process with application to the hypothesis test on the probability that X< Y