Estimation of copula models with discrete margins via Bayesian data augmentation

Smith, Michael S. and Khaled, Mohamad A. (2012) Estimation of copula models with discrete margins via Bayesian data augmentation. Journal of the American Statistical Association, 107 497: 290-303. doi:10.1080/01621459.2011.644501

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Author Smith, Michael S.
Khaled, Mohamad A.
Title Estimation of copula models with discrete margins via Bayesian data augmentation
Journal name Journal of the American Statistical Association   Check publisher's open access policy
ISSN 0162-1459
Publication date 2012-03-01
Sub-type Article (original research)
DOI 10.1080/01621459.2011.644501
Open Access Status DOI
Volume 107
Issue 497
Start page 290
End page 303
Total pages 14
Place of publication Alexandria, VA, United States
Publisher American Statistical Association
Language eng
Abstract Estimation of copula models with discrete margins can be difficult beyond the bivariate case. We show how this can be achieved by augmenting the likelihood with continuous latent variables, and computing inference using the resulting augmented posterior. To evaluate this, we propose two efficient Markov chain Monte Carlo sampling schemes. One generates the latent variables as a block using a Metropolis-Hastings step with a proposal that is close to its target distribution, the other generates them one at a time. Our method applies to all parametric copulas where the conditional copula functions can be evaluated, not just elliptical copulas as in much previous work. Moreover, the copula parameters can be estimated joint with any marginal parameters, and Bayesian selection ideas can be employed. We establish the effectiveness of the estimation method by modeling consumer behavior in online retail using Archimedean and Gaussian copulas. The example shows that elliptical copulas can be poor at modeling dependence in discrete data, just as they can be in the continuous case. To demonstrate the potential in higher dimensions, we estimate 16-dimensional D-vine copulas for a longitudinal model of usage of a bicycle path in the city of Melbourne, Australia. The estimates reveal an interesting serial dependence structure that can be represented in a parsimonious fashion using Bayesian selection of independence pair-copula components. Finally, we extend our results and method to the case where some margins are discrete and others continuous. Supplemental materials for the article are also available online.
Keyword Archimedean copula
Bayesian pair-copula selection
Discrete longitudinal data
Markov chain Monte Carlo
Multivariate dependence
Multivariate discrete data
Vine copulas
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Economics Publications
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Citation counts: TR Web of Science Citation Count  Cited 24 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 29 times in Scopus Article | Citations
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Created: Tue, 04 Jun 2013, 01:33:56 EST by Mohamad Khaled on behalf of Examinations