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Abstract
In this article we describe Bayesian nonparametric procedures for two-sample hypothesis
testing. Namely, given two sets of samples y^{(1)} iid F^{(1)} and y^{(2)} iid F^{(2)},
with F^{(1)}, F^{(2)} unknown, we wish to evaluate the evidence for the null hypothesis
H_{0}:F^{(1)} = F^{(2)} versus the alternative. Our method is based upon a nonparametric
Polya tree prior centered either subjectively or using an empirical procedure. We
show that the Polya tree prior leads to an analytic expression for the marginal likelihood
under the two hypotheses and hence an explicit measure of the probability of the null
Pr(H_{0}|y^{(1)},y^{(2)}).