MCMC Methods for Bayesian Mixtures of Copulas

Applications of copula models have been increasing in number in recent years. This class of models provides a modular parameterization of joint distributions: the specification of the marginal distributions is parameterized separately from the dependence structure of the joint, a convenient way of encoding a model for domains such as finance. Some recent advances on how to specify copulas for arbitrary dimensions have been proposed, by means of mixtures of decomposable graphical models. This paper introduces a Bayesian approach for dealing with mixtures of copulas which, due to the lack of prior conjugacy, raise computational challenges. We motivate and present families of Markov chain Monte Carlo (MCMC) proposals that exploit the particular structure of mixtures of copulas. Different algorithms are evaluated according to their mixing properties, and an application in financial forecasting with missing data illustrates the usefulness of the methodology.