# A Bayesian Semiparametric Gaussian Copula Approach to a Multivariate Normality Test

## TL;DR

This paper introduces a Bayesian semiparametric method combining Dirichlet processes and Gaussian copulas to test multivariate normality, demonstrating strong performance on simulated and real data.

## Contribution

It develops a novel Bayesian multivariate normality test using a copula approach with theoretical insights and practical validation.

## Key findings

- Excellent performance on simulated data
- Effective detection of non-normality in real data
- Theoretical properties established for the method

## Abstract

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.