Grid-Uniform Copulas and Rectangle Exchanges: Model and Bayesian Inference for a Rich Class of Copula Functions

• Activity Number: 225 - Recent Advances in Bayesian Methods for Complex Data Structures
• Type: Invited
• Date/Time: Wednesday, August 11, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Alejandro Jara*
• Companies: Pontificia Universidad Católica de Chile
• Keywords: Random probability distributions; Bayesian nonparametrics; Association modelling; Multivariate density estimation

Abstract

Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to form a joint distribution. Choosing a class of copula models is not a trivial task, which can be simplified by relying on rich classes of copula functions. We introduce a novel class of grid-uniform copula functions here, which is dense (in the Hellinger sense) in the space of all continuous copula functions. We propose a Bayesian model based on this class and develop an efficient Markov chain Monte Carlo algorithm for exploring the corresponding posterior distribution in arbitrarily many dimensions, allowing for the semiparametric or nonparametric modelling of continuous joint distributions. The methodology is illustrated by means of simulated and real-life data. Joint work with Nicolás Kuschinski. A. Jara's and N. Kuschinski's research was funded by ANID – Millennium Science Initiative Program – NCN17_059. A. Jara is also supported by Fondecyt grant 1180640.