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Biometrika Advance Access originally published online on May 4, 2009
Biometrika 2009 96(3):497-512; doi:10.1093/biomet/asp017
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© 2009 Biometrika Trust

Article

Objective Bayesian model selection in Gaussian graphical models

C. M. Carvalho

Booth School of Business, University of Chicago, Chicago, Illinois 60637, U.S.A. carlos.carvalho{at}chicagobooth.edu

J. G. Scott

Department of Statistical Science, Duke University, Durham, North Carolina 27708, U.S.A. james{at}stat.duke.edu

Received for publication 1 September 2007. Revision received 1 November 2008.
  Abstract

This paper presents a default model-selection procedure for Gaussian graphical models that involves two new developments. First, we develop a default version of the hyper-inverse Wishart prior for restricted covariance matrices, called the hyper-inverse Wishart g-prior, and show how it corresponds to the implied fractional prior for selecting a graph using fractional Bayes factors. Second, we apply a class of priors that automatically handles the problem of multiple hypothesis testing. We demonstrate our methods on a variety of simulated examples, concluding with a real example analyzing covariation in mutual-fund returns. These studies reveal that the combined use of a multiplicity-correction prior on graphs and fractional Bayes factors for computing marginal likelihoods yields better performance than existing Bayesian methods.

Key Words: Bayesian model selection • Fractional Bayes factor • Gaussian graphical model • Hyper-inverse Wishart distribution • Multiple hypothesis testing


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