  In recent years, conditional copulas, that allow dependence between variables
to vary according to the values of one or more covariates, have attracted
increasing attention. In high dimension, vine copulas offer greater flexibility
compared to multivariate copulas, since they are constructed using bivariate
copulas as building blocks. In this paper we present a novel inferential
approach for multivariate distributions, which combines the flexibility of vine
constructions with the advantages of Bayesian nonparametrics, not requiring the
specification of parametric families for each pair copula. Expressing
multivariate copulas using vines allows us to easily account for covariate
specifications driving the dependence between response variables. More
precisely, we specify the vine copula density as an infinite mixture of
Gaussian copulas, defining a Dirichlet process (DP) prior on the mixing
measure, and we perform posterior inference via Markov chain Monte Carlo (MCMC)
sampling. Our approach is successful as for clustering as well as for density
estimation. We carry out intensive simulation studies and apply the proposed
approach to investigate the impact of natural disasters on financial
development. Our results show that the methodology is able to capture the
heterogeneity in the dataset and to reveal different behaviours of different
country clusters in relation to natural disasters.
