Statistics and Computing

, Volume 18, Issue 3, pp 313–320

# Copula, marginal distributions and model selection: a Bayesian note

• Ralph dos Santos Silva
• Hedibert Freitas Lopes
Article

## Abstract

Copula functions and marginal distributions are combined to produce multivariate distributions. We show advantages of estimating all parameters of these models using the Bayesian approach, which can be done with standard Markov chain Monte Carlo algorithms. Deviance-based model selection criteria are also discussed when applied to copula models since they are invariant under monotone increasing transformations of the marginals. We focus on the deviance information criterion. The joint estimation takes into account all dependence structure of the parameters’ posterior distributions in our chosen model selection criteria. Two Monte Carlo studies are conducted to show that model identification improves when the model parameters are jointly estimated. We study the Bayesian estimation of all unknown quantities at once considering bivariate copula functions and three known marginal distributions.

## Keywords

Copula Deviance information criterion Marginal distribution Measure of dependence Monte Carlo study Skewness

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## Authors and Affiliations

• Ralph dos Santos Silva
• 1
Email author
• Hedibert Freitas Lopes
• 2
1. 1.Australian School of BusinessUniversity of New South WalesSydneyAustralia