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Biometrika 2003 90(4):809-830; doi:10.1093/biomet/90.4.809
© 2003 by Biometrika Trust
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Efficient estimation of covariance selection models

Frederick Wong1, Christopher K.Carter2 and Robert Kohn3

1 Australian Graduate School of Management, University of New South Wales, Sydney, NSW 2052, Australia fwong{at}agsm.edu.au 2 CSIRO Mathematical and Information Sciences, Locked Bag 17, North Ryde, Sydney, NSW 1670, Australia chris.carter{at}csiro.au 3 Faculty of Commerce and Economics, School of Economics, University of New South Wales, Sydney, NSW 2052, Australia r.kohn{at}unsw.edu.au

A Bayesian method is proposed for estimating an inverse covariance matrix from Gaussian data.The method is based on a prior that allows the off-diagonal elements of the inverse covariance matrix to be zero, and in many applications results in a parsimonious parameterisation of the covariance matrix. No assumption is made about the structure of the corresponding graphical model, so the method applies to both nondecomposable and decomposable graphs. All the parameters are estimated by model averaging using an efficient Metropolis–Hastings sampling scheme. A simulation study demonstrates that the method produces statistically efficient estimators of the covariance matrix, when the inverse covariance matrix is sparse. The methodology is illustrated by applying it to three examples that are high-dimensional relative to the sample size.

Key Words: Bayesian estimation; Gaussian graphical model; Model averaging; Multivariate regression; Partial correlation

Received November 2001. Revised August 2002


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