Dirichlet Process Mixture of Elliptical Copulas

• Activity Number: 404 - Bayesian Clustering and Classification
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jiali Wang* and Anton Westveld and Bronwyn Loong
• Companies: The Australian National University and The Australian National University and The Australian National University
• Keywords: Bayesian ; Nonparametric ; Missing data

Abstract

Copula-based methods provide a flexible approach to analyse multivariate data of mixed types. However, the choice of copula function is an open question. We consider a Bayesian nonparametric approach by using an infinite mixture of elliptical copulas induced by Dirichlet process mixture to build a flexible copula function. A slice sampling algorithm is used to sample from the infinite dimensional parameter space. We extend the work on prior parallel tempering used in finite mixture models to the Dirichlet process mixture model to overcome the mixing issue in multimodal distributions. Using simulations, we illustrate that the infinite mixture copula model performs better to capture tail dependence features of the data, and provides a better fit overall compared to their single component counterparts. We also apply the infinite mixture of copulas model as an imputation engine when there are missing data involved, and simulations show that they achieve better imputation accuracy especially for discrete variables. The proposed model is applied to a medical data set of acute stroke patients in Australia.