Bayesian Nonparametric Modeling 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. However, the literature mainly focused on the bivariate case, since the constraints on the multivariate copulas correlation matrices would make the specifications of covariates arduous. In high dimension, vine copulas offer greater flexibility compared to multivariate copulas, since they are constructed using bivariate copulas as building blocks. 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. We specify the vine copula density as an infinite mixture of Gaussian copulas, defining a Dirichlet process prior on the mixing measure, and performing posterior inference via Markov chain Monte Carlo sampling. Our approach is successful as for clustering as well as for density estimation. We carry out simulation studies and apply the proposed approach to analyze a veterinary dataset and to investigate the impact of natural disasters on financial development. Supplementary materials for this article are available online.

KEYWORD:

• Conditional copulas
• Dirichlet process prior
• Heterogeneity
• MCMC
• Mixtures
• Vine copulas

Disclosure Statement

The authors report there are no competing interests to declare.

Acknowledgments

The authors are grateful to the Editor, Associate Editor and Reviewers for their comments which have considerably improved the quality of the article. The authors also thanks Prof. Elena De Giuli, for stimulating discussions on an earlier version of the article, and Lu Lu for kindly sharing the R code of the model developed by her.

Additional information

Funding

The second author was supported by EPSRC project Dependence Modeling with Vine Copulas for the Integration of Unstructured and Structured Data, grant number EP/W021986/1.