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Factor copula models have been recently proposed for describing the joint distribution of a large number of variables in terms of a few common latent factors. A Bayesian procedure is employed in order to make fast inferences for multi-factor and structured factor copulas. To deal with the high dimensional structure, a Variational Inference (VI) algorithm is applied to estimate different specifications of factor copula models. Compared to the Markov Chain Monte Carlo (MCMC) approach, the variational approximation is much faster and could handle a sizeable problem in limited time. Another issue of factor copula models is that the bivariate copula functions connecting the variables are unknown in high dimensions. An automatic procedure is derived to recover the hidden dependence structure. By taking advantage of the posterior modes of the latent variables, the bivariate copula functions are selected by minimizing the Bayesian Information Criterion (BIC). Simulation studies in different contexts show that the procedure of bivariate copula selection could be very accurate in comparison to the true generated copula model. The proposed procedure is illustrated with two high dimensional real data sets.
factor copulas; model selection; variational inference