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Biometrika 2006 93(3):537-554; doi:10.1093/biomet/93.3.537
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© 2006 Biometrika Trust

Efficient Bayesian inference for Gaussian copula regression models

Michael Pitt1, David Chan2 and Robert Kohn3

1 Department of Economics, University of Warwick, Coventry CV4 7AL, U.K. m.pitt{at}warwick.ac.uk, 2 Cendant Corporation, Parsippany, New Jersey 07054, U.S.A. davidxchan{at}yahoo.com, 3 Faculty of Commerce and Economics, University of New South Wales, Sydney 2052, Australia. r.kohn{at}unsw.edu.au

A Gaussian copula regression model gives a tractable way of handling a multivariate regression when some of the marginal distributions are non-Gaussian. Our paper presents a general Bayesian approach for estimating a Gaussian copula model that can handle any combination of discrete and continuous marginals, and generalises Gaussian graphical models to the Gaussian copula framework. Posterior inference is carried out using a novel and efficient simulation method. The methods in the paper are applied to simulated and real data.

Key Words: Covariance selection; Graphical model; Markov chain Monte Carlo; Multivariate analysis; Non-Gaussian data.

Received November 2003. Revised February 2006.


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