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Journal of Probability and Statistics
Volume 2011 (2011), Article ID 152942, 10 pages
http://dx.doi.org/10.1155/2011/152942
Research Article

Gaussian Covariance Faithful Markov Trees

1Unité de Recherche Signaux et Systémes (U2S), Ecole Supérieure de la Statistique et de l'Analyse de l'Information (ESSAI), Ecole Nationale d'Ingénieurs de Tunis (ENIT), 6 Rue des Métiers, Charguia II 2035, Tunis Carthage, Ariana, Tunis 1002, Tunisia
2Department of Statistics, Department of Environmental Earth System Science, Woods Institute for the Environment, Stanford University, Standford, CA 94305, USA

Received 30 May 2011; Accepted 9 August 2011

Academic Editor: Junbin B. Gao

Copyright © 2011 Dhafer Malouche and Bala Rajaratnam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. R. Cox and N. Wermuth, Multivariate Dependencies, vol. 67 of Monographs on Statistics and Applied Probability, Chapman & Hall, London, UK, 1996.
  2. S. L. Lauritzen, Graphical Models, vol. 17 of Oxford Statistical Science Series, The Clarendon Press Oxford University Press, New York, NY, USA, 1996.
  3. J. Whittaker, Graphical Models in Applied Multivariate Statistics, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons Ltd., Chichester, UK, 1990.
  4. D. Edwards, Introduction to Graphical Modelling, Springer Texts in Statistics, Springer, New York, NY, USA, 2nd edition, 2000.
  5. B. Rajaratnam, H. Massam, and C. M. Carvalho, “Flexible covariance estimation in graphical Gaussian models,” The Annals of Statistics, vol. 36, no. 6, pp. 2818–2849, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. G. Kauermann, “On a dualization of graphical Gaussian models,” Scandinavian Journal of Statistics, vol. 23, no. 1, pp. 105–116, 1996. View at Zentralblatt MATH
  7. M. Banerjee and T. Richardson, “On a dualization of graphical Gaussian models: a correction note,” Scandinavian Journal of Statistics, vol. 30, no. 4, pp. 817–820, 2003.
  8. N. Wermuth, D. R. Cox, and G. M. Marchetti, “Covariance chains,” Bernoulli, vol. 12, no. 5, pp. 841–862, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. D. Malouche, “Determining full conditional independence by low-order conditioning,” Bernoulli, vol. 15, no. 4, pp. 1179–1189, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. K. Khare and B. Rajaratnam, “Covariance trees and Wishart distributions on cones,” in Algebraic Methods in Statistics and Probability II, vol. 516 of Contemporary Mathematics, pp. 215–223, American Mathematical Society, Providence, RI, USA, 2010.
  11. K. Khare and B. Rajaratnam, “Wishart distributions for decomposable covariance graph models,” The Annals of Statistics, vol. 39, no. 1, pp. 514–555, 2011. View at Publisher · View at Google Scholar
  12. M. Studený, Probabilistic Conditional Independence Structures, Springer, New York, NY, USA, 2004.
  13. A. Becker, D. Geiger, and C. Meek, “Perfect tree-like Markovian distributions,” Probability and Mathematical Statistics, vol. 25, no. 2, pp. 231–239, 2005. View at Zentralblatt MATH
  14. R. A. Brualdi and D. Cvetkovic, A Combinatorial Approach to Matrix Theory and Its Applications, Chapman & Hall/CRC, New York, NY, USA, 2008.
  15. B. Jones and M. West, “Covariance decomposition in undirected Gaussian graphical models,” Biometrika, vol. 92, no. 4, pp. 779–786, 2005. View at Publisher · View at Google Scholar