  In this work we propose a semiparametric bivariate copula whose density is
defined by a piecewise constant function on disjoint squares. We obtain the
maximum likelihood estimators of model parameters and prove that they reduce to
the sample copula under specific conditions. We further propose to carry out a
full Bayesian analysis of the model and introduce a spatial dependent prior
distribution for the model parameters. This prior allows the parameters to
borrow strength across neighbouring regions to produce smooth posterior
estimates. To characterise the posterior distribution, via the full conditional
distributions, we propose a data augmentation technique. A Metropolis-Hastings
step is required and we propose a novel adaptation scheme for the random walk
proposal distribution. We implement a simulation study and an analysis of a
real dataset to illustrate the performance of our model and inference
algorithms.
