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：典型的统计假设问题是两样假设测试,我们测试两种观察样本是否来自同一分布或两种不同的分布。然而,进行这一测试的标准方法要求在两个数据样本上进行强有力的分布假设。我们建议对两样假设测试问题采用半巴伊色非参数(半巴伊色非参数(semi-BNP)程序。首先,我们将得出一种新颖的BNP最大平均差异(MMD)测量假设测试。接下来,我们将表明我们提议的测试将产生一个较小的错误拒绝和接受公关率,从而优于常见MMMD方法。最后,我们将表明,我们可以将我们提议的假设测试程序嵌入一个基因对抗网络(GAN)框架,作为我们方法的应用。利用我们的新式的BNP假设测试,这种新的GAN方法可以帮助减轻所产生样品中缺乏的多样性,并产生比传统技术更准确的推断算法。</s>