  We propose a non-parametric, 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 does not require priors for high-dimensional parameter
vectors as do other nonparametric Bayesian procedures. We provide evidence that
the new procedure provides more stable Bayes factors than do methods based on
P\'olya trees. Somewhat surprisingly, the behavior of the proposed Bayes
factors when the two distributions are the same is usually superior to that of
P\'olya 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.
