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Two-sample Bayesian nonparametric hypothesis testing

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)}).
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https://hal.inria.fr/hal-00733547
Contributor : Francois Caron <>
Submitted on : Tuesday, September 18, 2012 - 8:25:48 PM
Last modification on : Thursday, June 18, 2020 - 12:32:04 PM

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  • HAL Id : hal-00733547, version 1

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Chris Holmes, Francois Caron, Jim Griffin, David A Stephens. Two-sample Bayesian nonparametric hypothesis testing. [Research Report] 2009. ⟨hal-00733547⟩

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