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

TL;DR

This paper introduces a new class of grid-uniform copula functions that are dense in the space of continuous copulas, along with a Bayesian inference method and MCMC algorithm, enhancing modeling flexibility for multivariate distributions.

Contribution

It presents a novel, dense class of copula functions and a Bayesian framework with an MCMC algorithm for improved dependence modeling.

Findings

The proposed copula class is dense in all continuous copulas.

The Bayesian model effectively captures dependence structures.

The MCMC algorithm facilitates efficient posterior exploration.

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 and its misspecification can lead to wrong conclusions. We introduce a novel class of grid-uniform copula functions, which is dense in the space of all continuous copula functions in a Hellinger sense. We propose a Bayesian model based on this class and develop an automatic Markov chain Monte Carlo algorithm for exploring the corresponding posterior distribution. The methodology is illustrated by means of simulated data and compared to the main existing approach.