An alternative bayesian approach to the multivariate behrens-fisher problem

In this note, an alternative approach to the multivariate Behrens-Fisher problem is presented in the Bayesian setup. We use the Kullback-Leibler di-vergence measure to assess the discrepancy between the “null” model and the “alternative” model. We then use the Bayesian approach to minimize the posterior expectation of the distance between the two models. A simulation study using bootstrap methods in the bivariate case is presented to demonstrate the implementation of the test procedure derived.