Bayesian model selection of vine copulas: a loss-based perspective

2026-06-19

AI Summary

This study addresses the computational challenges and intractable model space inherent in high-dimensional Bayesian vine copula model selection. The authors propose a novel framework that integrates loss-driven priors with shotgun stochastic search to simultaneously identify vine structures, select copula families, and estimate parameters. By employing a loss-guided sparse prior to shrink the model space and leveraging an efficient random search strategy, the method substantially enhances computational feasibility and efficiency in high-dimensional settings. Empirical evaluations on both simulated data and real-world ETF asset returns demonstrate that the proposed approach achieves estimation accuracy comparable to existing methods while offering markedly superior computational performance.

Abstract

The growing popularity of vine copulas in multivariate statistical analysis is largely driven by their ability to capture complex dependence structures. However, this flexibility comes at a cost, as the number of possible vine models grows rapidly and becomes intractable even in moderately low-dimensional settings. These limitations affect the practical applicability of current Bayesian inference and model selection approaches, effectively restricting it to problems of relatively small-dimension due to their high computational cost. This paper addresses the still open challenge of efficient model selection and estimation in Bayesian vine methodology. We propose a novel framework for Bayesian vine copula model selection that combines loss-based model priors with the shotgun stochastic search strategy. The strength of the proposed approach is twofold: it promotes sparsity and enables fast and effective structure selection. Furthermore, our comprehensive framework jointly identifies the vine structure, selects the copula families, and estimates the model parameters. The power of the proposed approach is demonstrated via simulation studies and an application to a real dataset of EFT portfolio asset returns.

Problem

• Bayesian model selection
• vine copulas
• high-dimensional dependence
• computational tractability
• model complexity

Innovation

• vine copulas
• Bayesian model selection
• loss-based priors
• shotgun stochastic search
• sparsity