Two-sample Bayesian Nonparametric Hypothesis Testing

作者：Holmes Chris C^*; Caron Francois; Griffin Jim E; Stephens David A

来源：Bayesian Analysis, 2015, 10(2): 297-320.

DOI：10.1214/14-BA914

• Bayesian nonparametrics
• Polya tree
• hypothesis testing

In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples y((1)) <(iid) under tilde> F-(1) and y((2)) <(iid) under tilde> F-(2), with F-(1), F-(2) unknown, we wish to evaluate the evidence for the null hypothesis H-0 : F-(1) equivalent to F-(2) versus the alternative H-1 : F-(1) not equal F-(2). 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 vertical bar{y((1)), y((2))}).

• 出版日期2015-6