Grid-uniform copulas and rectangle exchanges: Bayesian model and inference for a rich class of copula functions

Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to form a joint distribution. Choosing a class of copula models is not a trivial task, but it can be simplified by relying on rich classes of copula functions. We introduce a novel class of grid-uniform copula functions here, which is dense (in the Hellinger sense) in the space of all continuous copula functions. We propose a Bayesian model based on this class and develop an efficient Markov chain Monte Carlo algorithm for exploring the corresponding posterior distribution in arbitrarily many dimensions, allowing for the flexible modelling of continuous joint distributions. The methodology is illustrated by means of simulated data. Joint work with Nicolás Kuschinski.