Generalised bayesian sample copula of order $m$

In this work we propose a semiparametric bivariate copula whose density is defined by a picewise constant function on disjoint squares. We obtain the maximum likelihood estimators which reduce to the sample copula under specific conditions. We carry out a full Bayesian analysis of the model and propose 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. We implement a simulation study and illustrate the performance of our model with a real dataset.