Bayesian Copula Density Estimation Using Bernstein Yett-Uniform Priors

TL;DR

This paper introduces a new Bayesian approach for density estimation using Bernstein copulas, providing flexible modeling of multivariate distributions with separate marginal and dependence structures, supported by MCMC algorithms and demonstrated on data.

Contribution

It proposes a novel class of Bernstein copula functions with theoretical support analysis and develops MCMC methods for posterior exploration, advancing copula-based density estimation.

Findings

The proposed model effectively captures complex dependence structures.

MCMC algorithms facilitate efficient posterior sampling.

Method demonstrated successfully on simulated and real datasets.

Abstract

Probability density estimation is a central task in statistics. 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 random Bernstein copula functions, and studied its support and the behavior of its posterior distribution. The proposal is based on a particular class of random grid-uniform copulas, referred to as yett-uniform copulas. Alternative Markov chain Monte Carlo algorithms for exploring the posterior distribution under the proposed model are also studied. The methodology is illustrated by means of simulated and real data.