Multivariate <scp>C</scp>opula <scp>A</scp>nalysis <scp>T</scp>oolbox (MvCAT): Describing dependence and underlying uncertainty using a <scp>B</scp>ayesian framework

TLDR

The paper introduces MvCAT, a toolbox that offers a Bayesian framework for estimating predictive uncertainties of copulas, a hybrid‑evolution MCMC algorithm for posterior inference, and a platform for exploring diverse copula families. MvCAT implements a Bayesian inference scheme using a residual‑based Gaussian likelihood and a hybrid‑evolution Markov chain Monte Carlo algorithm to estimate copula parameters and quantify uncertainty. The toolbox demonstrates that local optimization methods often converge to suboptimal solutions, whereas the Bayesian approach in MvCAT overcomes this issue, better captures dependence structures, and allows uncertainty assessment as a function of record length.

Abstract

Abstract We present a newly developed Multivariate Copula Analysis Toolbox (MvCAT) which includes a wide range of copula families with different levels of complexity. MvCAT employs a Bayesian framework with a residual‐based Gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties. The contribution of this paper is threefold: (a) providing a Bayesian framework to approximate the predictive uncertainties of fitted copulas, (b) introducing a hybrid‐evolution Markov Chain Monte Carlo (MCMC) approach designed for numerical estimation of the posterior distribution of copula parameters, and (c) enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties. We show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima. The proposed method, however, addresses this limitation and improves describing the dependence structure. MvCAT also enables evaluation of uncertainties relative to the length of record, which is fundamental to a wide range of applications such as multivariate frequency analysis.