Bayesian Estimation of Pair Copula Constructions with Discrete Margins

• Activity Number: 302
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Anastasios Nicholas Panagiotelis*+ and Claudia Czado
• Companies: Technische Universitaet Muenchen and Technische Universitaet Muenchen
• Keywords: Copulas ; Discrete data ; Grouped move multigrid MCMC ; Pair copula constructions

Abstract

Copulas enable the construction of multivariate distributions that flexibly capture non-linear dependence and have fixed margins that are either continuous, discrete or some combination of both. For an m-dimensional model with discrete margins, maximum likelihood estimation is infeasible since computing the probability mass function requires 2^m evaluations of the copula function. We develop an approach based on introducing latent variables and jointly estimating copula and marginal parameters by Markov chain Monte Carlo (MCMC). This approach can be applied to wide range of copulas. In a simulated setting, we compare the computational speed and mixing of the Markov chain of different sampling schemes including grouped move multigrid MCMC samplers. As demonstrations we fit a flexible D-vine pair copula construction to medical, marketing and financial data.