  In this paper, we propose novel, fully Bayesian non-parametric tests for
one-sample and two-sample multivariate location problems. We model the
underlying distribution using a Dirichlet process prior, and develop a testing
procedure based on the posterior credible region for the spatial median
functional of the distribution. For the one-sample problem, we fail to reject
the null hypothesis if the credible set contains the null value. For the
two-sample problem, we form a credible set for the difference of the spatial
medians of the two samples and we fail to reject the null hypothesis of
equality if the credible set contains zero. We derive the local asymptotic
power of the tests under shrinking alternatives, and also present a simulation
study to compare the finite-sample performance of our testing procedures with
existing parametric and non-parametric tests.
