In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes

Conditional copula models are flexible tools for modelling complex dependence structures in regression settings. We construct Bayesian inference for the conditional copula model adapted to regression settings in which the bivariate outcome is continuous or mixed. The dependence between the copula parameter and the covariate is modelled using cubic splines. The proposed joint Bayesian inference is carried out using adaptive Markov chain Monte Carlo sampling. The deviance information criterion (DIC) is used for selecting the copula family that best approximates the data and for choosing the calibration function. The performances of the estimation and model selection methods are investigated using simulations.