0910.5060Oct 27, 2009Published at http://dx.doi.org/10.1214/14-BA914 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/)
In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples y(1)iid imF(1) and y(2)
Nearby in the stack
iid∼
F(2)
, with
F(1),F(2)
unknown, we wish to evaluate the evidence for the null hypothesis
H0:F(1)≡F(2)
versus the alternative
H1:F(1)=F(2)
. Our method is based upon a nonparametric Pólya tree prior centered either subjectively or using an empirical procedure. We show that the Pólya 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(H0∣{y(1),y(2)})
.
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