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Title: A class of random Bernstein copula models Authors:  Alejandro Jara - Pontificia Universidad Catolica de Chile (Chile) [presenting]
Abstract: Copula models provide great flexibility in modeling relationships between random variables. For inference to take full advantage of this flexibility, one needs appropriately rich families of copula functions, capable of approximating any copula. One such family is the family of Bernstein copulas, which are a variety of multivariate Bernstein polynomial, and which has been shown to be dense in the space of continuous copula functions. Bernstein copulas have been used for inference before, but only using likelihood-free approximation methods. We observe a fact about the geometry of the parameter space of Bernstein copulas, and note that it is closely related to a different class of copula known as grid uniform copulas. Based on this relationship, we propose a Bayesian model based on Bernstein copulas and an automatic MCMC algorithm capable of performing full posterior inference on the copula and marginal distributions.