Markov chain Monte Carlo

Quantum mechanics

Copula (linguistics)

Algorithm

Gaussian

Engineering

Bayesian probability

Aerospace engineering

Statistics

Multivariate statistics

Multivariate normal distribution

Markov chain

Range (aeronautics)

Computer science

Mathematical optimization

Physics

Mathematics

Maxima and minima

Econometrics

Mathematical analysis

Artificial intelligence

Machine learning

Water Resources Research

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.

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

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