A classic inferential problem in statistics is the two-sample hypothesis test, where we test whether two samples of observations are either drawn from the same distribution or two distinct distributions. However, standard methods for performing this test require strong distributional assumptions on the two samples of data. We propose a semi-Bayesian nonparametric (semi-BNP) procedure for the two-sample hypothesis testing problem. First, we will derive a novel BNP maximum mean discrepancy (MMD) measure-based hypothesis test. Next, we will show that our proposed test will outperform frequentist MMD-based methods by yielding a smaller false rejection and acceptance rate of the null. Finally, we will show that we can embed our proposed hypothesis testing procedure within a generative adversarial network (GAN) framework as an application of our method. Using our novel BNP hypothesis test, this new GAN approach can help to mitigate the lack of diversity in the generated samples and produce a more accurate inferential algorithm compared to traditional techniques.

翻译：统计学中的一个经典推断问题是双样本假设检验，即检验两组观测样本是否来自同一分布或两个不同的分布。然而，执行该检验的标准方法需要对两组数据样本做出较强的分布假设。我们针对双样本假设检验问题提出了一种半贝叶斯非参数（semi-BNP）程序。首先，我们将推导一种基于新型BNP最大均值差异（MMD）度量的假设检验。其次，我们将证明，与基于频率学派的MMD方法相比，我们提出的检验能降低原假设的错误拒绝率和错误接受率。最后，我们将展示如何将我们所提出的假设检验程序嵌入生成对抗网络（GAN）框架中，作为该方法的一种应用。通过使用这种新型的BNP假设检验，相较于传统技术，该GAN方法有助于缓解生成样本多样性不足的问题，并产生更准确的推断算法。