In recent years, Bayesian nonparametric statistics has gathered extraordinary
attention. Nonetheless, a relatively little amount of work has been expended on
Bayesian nonparametric hypothesis testing. In this paper, a novel Bayesian
nonparametric approach to the two-sample problem is established. Precisely,
given two samples X=X1​,…,Xm1​​∼i.i.d.F
and Y=Y1​,…,Ym2​​∼i.i.d.G, with F and G
being unknown continuous cumulative distribution functions, we wish to test the
null hypothesis H0​: F=G. The method is based on the Kolmogorov
distance and approximate samples from the Dirichlet process centered at the
standard normal distribution and a concentration parameter 1. It is
demonstrated that the proposed test is robust with respect to any prior
specification of the Dirichlet process. A power comparison with several
well-known tests is incorporated. In particular, the proposed test dominates
the standard Kolmogorov-Smirnov test in all the cases examined in the paper.Comment: 25 pages, 8 figure