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We propose a non-parametric, two-sample Bayesian test for checking whether ornot two data sets share a common distribution. The test makes use of datasplitting ideas and does not require priors for high-dimensional parametervectors as do other nonparametric Bayesian procedures. We provide evidence thatthe new procedure provides more stable Bayes factors than do methods based onP\'olya trees. Somewhat surprisingly, the behavior of the proposed Bayesfactors when the two distributions are the same is usually superior to that ofP\'olya tree Bayes factors. We showcase the effectiveness of the test byproving its consistency, conducting a simulation study and applying the test toHiggs boson data.

Use of Cross-validation Bayes Factors to Test Equality of Two Densities