MCMC Methods for Bayesian Mixtures of Copulas

Ricardo Silva, Robert Gramacy
; Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, PMLR 5:512-519, 2009.

Abstract

Applications of copula models have been increasing in number in recent years. This class of models provides a modular parameterization of joint distributions: the specification of the marginal distributions is parameterized separately from the dependence structure of the joint, a convenient way of encoding a model for domains such as finance. Some recent advances on how to specify copulas for arbitrary dimensions have been proposed, by means of mixtures of decomposable graphical models. This paper introduces a Bayesian approach for dealing with mixtures of copulas which, due to the lack of prior conjugacy, raise computational challenges. We motivate and present families of Markov chain Monte Carlo (MCMC) proposals that exploit the particular structure of mixtures of copulas. Different algorithms are evaluated according to their mixing properties, and an application in financial forecasting with missing data illustrates the usefulness of the methodology.

Cite this Paper


BibTeX
@InProceedings{pmlr-v5-silva09a, title = {MCMC Methods for Bayesian Mixtures of Copulas}, author = {Ricardo Silva and Robert Gramacy}, booktitle = {Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics}, pages = {512--519}, year = {2009}, editor = {David van Dyk and Max Welling}, volume = {5}, series = {Proceedings of Machine Learning Research}, address = {Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v5/silva09a/silva09a.pdf}, url = {http://proceedings.mlr.press/v5/silva09a.html}, abstract = {Applications of copula models have been increasing in number in recent years. This class of models provides a modular parameterization of joint distributions: the specification of the marginal distributions is parameterized separately from the dependence structure of the joint, a convenient way of encoding a model for domains such as finance. Some recent advances on how to specify copulas for arbitrary dimensions have been proposed, by means of mixtures of decomposable graphical models. This paper introduces a Bayesian approach for dealing with mixtures of copulas which, due to the lack of prior conjugacy, raise computational challenges. We motivate and present families of Markov chain Monte Carlo (MCMC) proposals that exploit the particular structure of mixtures of copulas. Different algorithms are evaluated according to their mixing properties, and an application in financial forecasting with missing data illustrates the usefulness of the methodology.} }
Endnote
%0 Conference Paper %T MCMC Methods for Bayesian Mixtures of Copulas %A Ricardo Silva %A Robert Gramacy %B Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2009 %E David van Dyk %E Max Welling %F pmlr-v5-silva09a %I PMLR %J Proceedings of Machine Learning Research %P 512--519 %U http://proceedings.mlr.press %V 5 %W PMLR %X Applications of copula models have been increasing in number in recent years. This class of models provides a modular parameterization of joint distributions: the specification of the marginal distributions is parameterized separately from the dependence structure of the joint, a convenient way of encoding a model for domains such as finance. Some recent advances on how to specify copulas for arbitrary dimensions have been proposed, by means of mixtures of decomposable graphical models. This paper introduces a Bayesian approach for dealing with mixtures of copulas which, due to the lack of prior conjugacy, raise computational challenges. We motivate and present families of Markov chain Monte Carlo (MCMC) proposals that exploit the particular structure of mixtures of copulas. Different algorithms are evaluated according to their mixing properties, and an application in financial forecasting with missing data illustrates the usefulness of the methodology.
RIS
TY - CPAPER TI - MCMC Methods for Bayesian Mixtures of Copulas AU - Ricardo Silva AU - Robert Gramacy BT - Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics PY - 2009/04/15 DA - 2009/04/15 ED - David van Dyk ED - Max Welling ID - pmlr-v5-silva09a PB - PMLR SP - 512 DP - PMLR EP - 519 L1 - http://proceedings.mlr.press/v5/silva09a/silva09a.pdf UR - http://proceedings.mlr.press/v5/silva09a.html AB - Applications of copula models have been increasing in number in recent years. This class of models provides a modular parameterization of joint distributions: the specification of the marginal distributions is parameterized separately from the dependence structure of the joint, a convenient way of encoding a model for domains such as finance. Some recent advances on how to specify copulas for arbitrary dimensions have been proposed, by means of mixtures of decomposable graphical models. This paper introduces a Bayesian approach for dealing with mixtures of copulas which, due to the lack of prior conjugacy, raise computational challenges. We motivate and present families of Markov chain Monte Carlo (MCMC) proposals that exploit the particular structure of mixtures of copulas. Different algorithms are evaluated according to their mixing properties, and an application in financial forecasting with missing data illustrates the usefulness of the methodology. ER -
APA
Silva, R. & Gramacy, R.. (2009). MCMC Methods for Bayesian Mixtures of Copulas. Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, in PMLR 5:512-519

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