Title: Approximate Bayesian conditional copulas
Authors: Clara Grazian - University of Sydney (Australia) [presenting]
Luciana Dalla Valle - University of Plymouth (United Kingdom)
Brunero Liseo - Sapienza Universita di Roma (Italy)
Abstract: Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem, any $d$-dimensional absolutely continuous distribution function can be uniquely represented as a copula, i.e. a joint cumulative distribution function on the unit hypercube with uniform marginals, which captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals; however, extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the conditional copula, especially when one does not have enough information to select the copula model. We will present and compare several Bayesian methods to approximate the posterior distribution of functionals of the dependence varying according to covariates; the main advantage of the methods investigated here is that they use nonparametric models, avoiding the selection of the copula, which is usually a delicate aspect of copula modelling. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics.