Conditional Copula models using loss-based Bayesian Additive Regression Trees

TL;DR

This paper introduces a semi-parametric Bayesian approach using BART for modeling complex, conditional dependencies between variables, with novel priors and algorithms to improve inference and reduce overfitting.

Contribution

It develops a loss-based prior for BART tree complexity and an adaptive Reversible Jump MCMC algorithm for efficient, flexible modeling of conditional copulas.

Findings

Successfully recovers true tree structures in simulations

Efficiently models complex, non-smooth likelihood functions

Provides case studies on economic and demographic data

Abstract

The study of dependence between random variables under external influences is a challenging problem in multivariate analysis. We address this by proposing a novel semi-parametric approach for conditional copula models using Bayesian additive regression trees (BART) models. BART is becoming a popular approach in statistical modelling due to its simple ensemble type formulation complemented by its ability to provide inferential insights. Although BART allows us to model complex functional relationships, it tends to suffer from overfitting. In this article, we exploit a loss-based prior for the tree topology that is designed to reduce the tree complexity. In addition, we propose a novel adaptive Reversible Jump Markov Chain Monte Carlo algorithm that is ergodic in nature and requires very few assumptions allowing us to model complex and non-smooth likelihood functions with ease. Moreover, we show that our method can efficiently recover the true tree structure and approximate a complex conditional copula parameter, and that our adaptive routine can explore the true likelihood region under a sub-optimal proposal variance. Lastly, we provide case studies concerning the effect of gross domestic product on the dependence between the life expectancies and literacy rates of the male and female populations of different countries.