Title: A new flexible Bayesian hypothesis test for multivariate data
Authors: Ivan Gutierrez - Pontificia Universidad Catolica de Chile (Chile) [presenting]
Danilo Alvares - Pontificia Universidad Catolica de Chile (Chile)
Luis Gutierrez - Pontificia Universidad Catolica de Chile (Chile)
Abstract: A Bayesian hypothesis testing procedure is proposed for comparing the multivariate distributions of several treatment groups against a control group. This test is based on a flexible model for the group distributions with the introduction of 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 prior distribution from the latent vector 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 this procedure with state-of-the-art alternatives. The 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 gains for rats. In both applications, we find relevant differences between the control group and at least one treatment group.