WIKS: A general Bayesian nonparametric index for quantifying differences between two populations


A key problem in many research investigations is to decide whether two samples have the same distribution. Numerous statistical methods have been devoted to this issue, but only few considered a Bayesian nonparametric approach. In this paper, we propose a novel nonparametric Bayesian index (WIKS) for quantifying the difference between two populations 𝑃1 and 𝑃2, which is defined by a weighted posterior expectation of the Kolmogorov–Smirnov distance between 𝑃1 and 𝑃2. We present a Bayesian decision-theoretic argument to support the use of WIKS index and a simple algorithm to compute it. Furthermore, we prove that WIKS is a statistically consistent procedure and that it controls the significance level uniformly over the null hypothesis, a feature that simplifies the choice of cutoff values for taking decisions. We present a real data analysis and an extensive simulation study showing that WIKS is more powerful than competing approaches under several settings.