Bayesian Nonparametric Modelling of Conditional Multidimensional Dependence Structures

Abstract

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.