Statistics and Computing

, Volume 19, Issue 3, pp 303–316 | Cite as

Bayesian covariance matrix estimation using a mixture of decomposable graphical models

  • Helen Armstrong
  • Christopher K. Carter
  • Kin Foon Kevin Wong
  • Robert Kohn
Article

Abstract

We present a Bayesian approach to estimating a covariance matrix by using a prior that is a mixture over all decomposable graphs, with the probability of each graph size specified by the user and graphs of equal size assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs in more efficiently estimating the covariance matrix. The prior requires knowing the number of decomposable graphs for each graph size and we give a simulation method for estimating these counts. We also present a Markov chain Monte Carlo method for estimating the posterior distribution of the covariance matrix that is much more efficient than current methods. Both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.

Keywords

Covariance selection Reduced conditional sampling Variable selection 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Helen Armstrong
    • 1
  • Christopher K. Carter
    • 2
  • Kin Foon Kevin Wong
    • 3
  • Robert Kohn
    • 2
  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia
  2. 2.Australian School of BusinessUniversity of New South WalesSydneyAustralia
  3. 3.Neuroscience Statistics Research LaboratoryMassachusetts General HospitalBostonUSA

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