Archimedean copula的贝叶斯非参数混合
Bayesian nonparametric mixtures of Archimedean copulas
AI总结：
本文提出了一种基于Poisson-Dirichlet过程的Archimedean copula贝叶斯非参数混合模型，以提升依赖性建模的灵活性，并通过数值实验验证了其有效性。
摘要：
基于copula的依赖性建模通常依赖参数化形式。这在数学上很方便，但当参数族不适合当前数据和模型时，可能在统计上效率低下。本文引入了Archimedean copula的贝叶斯非参数混合，以增加基于copula的依赖性建模的灵活性。具体而言，使用Poisson-Dirichlet过程作为Archimedean copula参数上的混合分布。研究了主要Archimedean族的混合模型性质，并通过其全条件分布对后验分布进行采样。通过涉及模拟和真实数据的数值实验展示了模型的性能。
英文摘要：
Copula-based dependence modeling often relies on parametric formulations. This is mathematically convenient, but can be statistically inefficient when the parametric families are not suitable for the data and model in focus. A Bayesian nonparametric mixture of Archimedean copulas is introduced to increase the flexibility of copula-based dependence modeling. Specifically, the Poisson-Dirichlet process is used as a mixing distribution over the Archimedean copulas' parameter. Properties of the mixture model are studied for the main Archimedean families, and posterior distributions are sampled via their full conditional distributions. The performance of the model is illustrated via numerical experiments involving simulated and real data.
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