In this paper, a Bayesian nonparametric approach to the two-sample problem is proposed. Given two samples \(\text{X} = {X_1}, \ldots ,{X_{m1}}\;\mathop {\text~}\limits^{i.i.d.} F\) and \(Y = {Y_1}, \ldots ,{Y_{{m_2}}}\mathop {\text~}\limits^{i.i.d.} G\), with F and G being unknown continuous cumulative distribution functions, we wish to test the null hypothesis H ₀: F = G. The method is based on computing the Kolmogorov distance between two posterior Dirichlet processes and comparing the results with a reference distance. The parameters of the Dirichlet processes are selected so that any discrepancy between the posterior distance and the reference distance is related to the difference between the two samples. Relevant theoretical properties of the procedure are also developed. Through simulated examples, the approach is compared to the frequentist Kolmogorov–Smirnov test and a Bayesian nonparametric test in which it demonstrates excellent performance.

中文翻译：

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使用贝叶斯非参数方法的两样本Kolmogorov-Smirnov检验

在本文中，提出了一种针对二样本问题的贝叶斯非参数方法。给定两个样本\（\ text {X} = {X_1}，\ ldots，{X_ {m1}} \; \ mathop {\ text〜} \ limits ^ {iid} F \）和\（Y = {Y_1} ，\ ldots，{Y _ {{m_2}}} \ mathop {\ text〜} \ limits ^ {iid} G \），其中F和G为未知的连续累积分布函数，我们希望检验原假设H ₀：F = G。该方法基于计算两个后Dirichlet过程之间的Kolmogorov距离，并将结果与​​参考距离进行比较。选择Dirichlet过程的参数，以使后距离和参考距离之间的任何差异都与两个样本之间的差异有关。该程序的相关理论特性也得到了发展。通过模拟示例，将该方法与经常使用的Kolmogorov–Smirnov检验和贝叶斯非参数检验进行了比较，这些检验证明了该方法的出色性能。