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Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):647-659; doi:10.1093/biomet/asm056
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Copyright © 2007 Biometrika Trust

Articles

Simulation of hyper-inverse Wishart distributions in graphical models

Carlos M. Carvalho

Department of Statistical Science, Duke University, Durham, North Carolina 27708-0251, U.S.A.

Hélène Massam

Department of Mathematics & Statistics, York University, Toronto M3 J1P3, Canada

Mike West

Department of Statistical Science, Duke University, Durham, North Carolina 27708-0251, U.S.A.

carlos{at}stat.duke.edu

massamh{at}mathstat.yorku.ca

mw{at}stat.duke.edu

Received for publication 1 May 2006. Revision received 1 January 2007.
  Abstract

We introduce and exemplify an efficient method for direct sampling from hyper-inverse Wishart distributions. The method relies very naturally on the use of standard junction-tree representation of graphs, and couples these with matrix results for inverse Wishart distributions. We describe the theory and resulting computational algorithms for both decomposable and nondecomposable graphical models. An example drawn from financial time series demonstrates application in a context where inferences on a structured covariance model are required. We discuss and investigate questions of scalability of the simulation methods to higher-dimensional distributions. The paper concludes with general comments about the approach, including its use in connection with existing Markov chain Monte Carlo methods that deal with uncertainty about the graphical model structure.

Key Words: Gaussian graphical model • Hyper-inverse Wishart • Junction tree • Portfolio analysis • Posterior simulation


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