A new flexible Bayesian hypothesis test for multivariate data

We propose a Bayesian hypothesis testing procedure for comparing the multivariate distributions of several treatment groups against a control group. This test is derived from a flexible model for the group distributions based on a random binary vector such that, if its jth element equals one, then the jth treatment group is merged with the control group. The group distributions' flexibility comes from a dependent Dirichlet process, while the latent vector prior distribution ensures a multiplicity correction to the testing procedure. We explore the posterior consistency of the Bayes factor and provide a Monte Carlo simulation study comparing the performance of our procedure with state-of-the-art alternatives. Our results show that the presented method performs better than competing approaches. Finally, we apply our proposal to two classical experiments. The first one studies the effects of tuberculosis vaccines on multiple health outcomes for rabbits, and the second one analyzes the effects of two drugs on weight gain for rats. In both applications, we find relevant differences between the control group and at least one treatment group.