Copula-based dependence modelling often relies on parametric formulations. This is mathematically convenient but can be statistically inefficient if the parametric families are not suitable for the data and model in focus. To improve the flexibility in modeling dependence, we consider a Bayesian nonparametric mixture model of Archimedean copulas which can capture complex dependence patterns and can be extended to arbitrary dimensions. In particular we use the Poisson-Dirichlet process as mixing distribution over the single parameter of the Archimedean copulas. Properties of the mixture model are studied for the main Archimedenan families and posterior distributions are sampled via their full conditional distributions. Performance of the model is via numerical experiments involving simulated and real data.

翻译：基于Copula的相依性建模通常依赖于参数化设定。这种方法在数学上较为便利，但当参数族不适用于所关注的数据和模型时，可能在统计上效率低下。为提高相依性建模的灵活性，本文提出一种基于阿基米德Copula的贝叶斯非参数混合模型，该模型能够捕捉复杂的相依模式，并可扩展至任意维度。特别地，我们采用泊松-狄利克雷过程作为阿基米德Copula单一参数的混合分布。针对主要阿基米德Copula族，本文研究了混合模型的性质，并通过完全条件分布对后验分布进行抽样。通过包含模拟数据和真实数据的数值实验，评估了模型的性能。