  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 and its misspecification can lead to wrong conclusions. We
introduce a novel class of grid-uniform copula functions, which is dense in the
space of all continuous copula functions in a Hellinger sense. We propose a
Bayesian model based on this class and develop an automatic Markov chain Monte
Carlo algorithm for exploring the corresponding posterior distribution. The
methodology is illustrated by means of simulated data and compared to the main
existing approach.
