  Determining if two histograms are consistent, whether they have been drawn
from the same underlying distribution or not, is a common problem in physics.
Existing approaches are not only limited in power but also inapplicable to
histograms filled with importance weights, a common feature of Monte Carlo
simulations. From a Bayesian perspective, the comparison between a single
underlying distribution and two underlying distributions is readily solved
within the context of model comparison. I introduce an implementation of
Bayesian model comparison to the problem, including the extension to importance
sampling.
