Approximate Bayesian methods for multivariate and conditional copulae

Abstract

We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution, where copula is a flexible probabilistic tool that allows the researcher to model the joint distribution of a random vector in two separate steps: the marginal distributions and a copula function which captures the dependence structure among the vector components. The method is also based on the properties of an approximate BayesianMonteCarlo algorithm, where the proposed values of the functional of interest areweighted in terms of their empirical likelihood. This method is particularly useful when the likelihood function associated with theworking model is too costly to evaluate or when the working model is only partially specified.