Copula, marginal distributions and model selection: a Bayesian note |
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Authors: | Ralph dos Santos Silva Hedibert Freitas Lopes |
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Institution: | (1) Australian School of Business, University of New South Wales, Sydney, 2052, Australia;(2) Graduate School of Business, University of Chicago, Chicago, 60637, USA |
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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. |
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Keywords: | Copula Deviance information criterion Marginal distribution Measure of dependence Monte Carlo study Skewness |
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