  Probability density estimation is a central task in statistics. 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 random Bernstein copula functions, and studied its
support and the behavior of its posterior distribution. The proposal is based
on a particular class of random grid-uniform copulas, referred to as
yett-uniform copulas. Alternative Markov chain Monte Carlo algorithms for
exploring the posterior distribution under the proposed model are also studied.
The methodology is illustrated by means of simulated and real data.
