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 \(P_1\) and \(P_2\), which is defined by a weighted posterior expectation of the Kolmogorov–Smirnov distance between \(P_1\) and \(P_2\). 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.

许多研究调查中的关键问题是确定两个样本是否具有相同的分布。许多统计方法致力于解决这一问题，但只有极少数被认为是贝叶斯非参数方法。在本文中，我们提出了一种新颖的非参数贝叶斯指数（WIKS），用于量化两个种群\（P_1 \）和\（P_2 \）之间的差异，该指数由加权加权后验期望\（之间的Kolmogorov–Smirnov距离来定义P_1 \）和\（P_2 \）。我们提出一个贝叶斯决策理论论据来支持WIKS索引的使用和一种简单的算法来计算它。此外，我们证明了WIKS是统计上一致的过程，并且在原假设上均匀地控制了显着性水平，该功能简化了用于决策的临界值的选择。我们提供了真实的数据分析和广泛的模拟研究，表明WIKS在某些情况下比竞争方法更强大。