Use of cross-validation Bayes factors to test equality of two densities

초록

We propose a nonparametric, two-sample Bayesian test for checking whether or not two data sets share a common distribution. The test makes use of data splitting ideas and requires only simple priors for the bandwidths of two kernel density estimates. Importantly, it does not require priors for high- or infinite-dimensional parameter vectors, as do other nonparametric Bayesian procedures. We provide evidence that the new procedure leads to more stable Bayes factors than do methods based on P & oacute;lya trees. Somewhat surprisingly, the behaviour of the proposed Bayes factors when the two distributions are the same is usually superior to that of P & oacute;lya tree Bayes factors. We showcase the effectiveness of the test by proving its consistency, conducting a simulation study and applying the test to Higgs Boson data.

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