Conditional Copula models using loss-based Bayesian Additive Regression Trees

2025-12-12

AI Summary

Addressing the challenge of modeling dynamic, nonsmooth multivariate dependence structures under external covariates, this paper proposes a loss-driven prior-based Bayesian additive regression trees (BART) framework for conditional copulas. Methodologically, it introduces a novel loss-guided tree topology prior and integrates an adaptive reversible-jump MCMC algorithm to efficiently explore high-dimensional, nonsmooth likelihoods while ensuring tree structure identifiability and consistent parameter estimation. Theoretically, we establish compatibility between model complexity control and valid statistical inference. Simulation studies demonstrate that the method accurately recovers true tree structures and closely approximates complex conditional copulas. Empirical analysis reveals a significant nonlinear moderating effect of GDP on cross-national dependence between gender-specific life expectancy and literacy rates.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Sustainability of Web economics

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.

Problem

• Modeling conditional dependence with Bayesian additive regression trees
• Reducing overfitting in BART using loss-based priors
• Developing adaptive MCMC for complex likelihood functions

Innovation

• Conditional copula models using Bayesian additive regression trees
• Loss-based prior reduces tree complexity to prevent overfitting
• Adaptive Reversible Jump MCMC algorithm for complex likelihood functions