In this paper, a Bayesian semiparametric copula approach is used to model the underlying multivariate distribution $F_{true}$. First, the Dirichlet process is constructed on the unknown marginal distributions of $F_{true}$. Then a Gaussian copula model is utilized to capture the dependence structure of $F_{true}$. As a result, a Bayesian multivariate normality test is developed by combining the relative belief ratio and the Energy distance. Several interesting theoretical results of the approach are derived. Finally, through several simulated examples and a real data set, the proposed approach reveals excellent performance.

中文翻译：

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多变量正态性检验的贝叶斯半参数高斯 copula 方法

在本文中，贝叶斯半参数 copula 方法用于对基础多元分布 $F_{true}$ 进行建模。首先，狄利克雷过程是在 $F_{true}$ 的未知边际分布上构建的。然后使用高斯 copula 模型来捕获 $F_{true}$ 的依赖结构。因此，通过结合相对置信比和能量距离开发了贝叶斯多元正态性检验。导出了该方法的几个有趣的理论结果。最后，通过几个模拟例子和一个真实的数据集，所提出的方法表现出优异的性能。