Computational aspects related to inference in gaussian graphical models with the G-Wishart prior

Journal of Computational and Graphical Statistics

Volumn 20, Issue 1, 2011, Pages 140-157

  Lenkoski, Alex ^a   Dobra, Adrian ^b  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Bayesian model averaging; Covariance estimation; Covariance selection; Multivariate regression; Stochastic search

Indexed keywords

EID: 79952783291     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2010.08181     Document Type: Article

References (41)

1. Asci, C., and Piccioni, M. (2007), "Functionally Compatible Local Characteristics for the Local Specification of Priors in Graphical Models," Scandinavian Journal of Statistics, 34, 829-840. [141,145]
2. Atay-Kayis, A., and Massam, H. (2005), "A Monte Carlo Method for Computing the Marginal Likelihood in Nondecomposable Gaussian Graphical Models," Biometrika, 92, 317-335. [141-143,146] (Pubitemid 40937638)
3. Barnard, J., McCulloch, R., and Meng, X. (2000), "Modeling Covariance Matrices in Terms of Standard Deviations and Correlations, With Application to Shrinkage," Statistica Sinica, 10, 1281-1311. [141]
4. Berger, J. O., and Molina, G. (2005), "Posterior Model Probabilities via Path-Based Pairwise Priors," Statistica Neerlandica, 59, 3-15. [148,149] (Pubitemid 40405922)
5. Bickel, P. J., and Levina, E. (2008), "Regularized Estimation of Large Covariance Matrices," The Annals of Statistics, 36, 199-227. [140,151]
6. Bron, C., and Kerboscht, J. (1973), "Algorithm 457: Finding All Cliques of an Undirected Graph," Communications of the ACM Archive, 16, 575-577. [144]
7. Carvalho, C. M., Massam, H., andWest, M. (2007), "Simulation of Hyper-Inverse Wishart Distributions in Graphical Models," Biometrika, 7, 269-281. [145]
8. Daniels, M., and Kass, R. (1999), "Nonconjugate Bayesian Estimation of Covariance Matrices," Journal of the American Statistical Association, 94, 1254-1263. [141]
9. Dawid, A. P., and Lauritzen, S. L. (1993), "Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models," The Annals of Statistics, 21, 1272-1317. [142,150]
10. Dellaportas, P., Giudici, P., and Roberts, G. (2003), "Bayesian Inference for Nondecomposable Graphical Gaussian Models," Sankhya, 65, 43-55. [141,143]
11. Dempster, A. P. (1972), "Covariance Selection," Biometrics, 28, 157-175. [140,141,143]
12. Diaconnis, P., and Ylvisaker, D. (1979), "Conjugate Priors for Exponential Families," The Annals of Statistics, 7, 269-281. [141,142]
13. Drton, M., and Perlman, M. D. (2004), "Model Selection for Gaussian Concentration Graphs," Biometrika, 91, 591-602. [141] (Pubitemid 41309895)
14. Edwards, D. M. (2000), Introduction to Graphical Modelling, New York: Springer. [141]
15. Giudici, P., and Green, P. J. (1999), "Decomposable Graphical Gaussian Model Determination," Biometrika, 86, 785-801. [141,147]
16. Green, P. J. (1995), "Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination," Biometrika, 82, 711-732. [147]
17. Harville, D. A. (1997), Matrix Algebra From a Statistician's Perspective, New York: Springer Science. [146]
18. Huang, J., Liu, N., Pourahmadi, M., and Liu, L. (2006), "Covariance Matrix Selection and Estimation via Penalized Normal Likelihood," Biometrika, 93, 85-98. [151]
19. Jones, B., Carvalho, C., Dobra, A., Hans, C., Carter, C., and West, M. (2005), "Experiments in Stochastic Computation for High-Dimensional Graphical Models," Statistical Science, 20, 388-400. [141,147,148] (Pubitemid 43266225)
20. Kass, R., and Raftery, A. E. (1995), "Bayes Factors," Journal of the American Statistical Association, 90, 773- 795. [141,146]
21. Knuiman, M. (1978), "Covariance Selection," Advances in Applied Probability, Special Supplement, 10, 123-130. [143]
22. Lauritzen, S. L. (1996), Graphical Models, Oxford, U.K.: Oxford University Press. [142,144]
23. Leonard, T., and Hsu, J. S. J. (1992), "Bayesian Inference for a Covariance Matrix," The Annals of Statistics, 20, 1669-1696. [141]
24. Letac, G., and Massam, H. (2007), "Wishart Distributions for Decomposable Graphs," The Annals of Statistics, 35, 1278-1323. [142]
25. Liechty, J. C., Liechty, M. W., and Müller, P. (2004), "Bayesian Correlation Estimation," Biometrika, 91, 1-14. [141] (Pubitemid 41309833)
26. Madigan, D., and York, J. (1995), "Bayesian Graphical Models for Discrete Data," International Statistical Review, 63, 215-232. [148]
27. Meinshausen, N., and Bühlmann, P. (2006), "High-Dimensional GraphsWith the Lasso," The Annals of Statistics, 34, 1436-1462. [140,141]
28. Muirhead, R. J. (2005), Aspects of Multivariate Statistical Theory, U.S.A.: Wiley. [143,145,150]
29. Piccioni, M. (2000), "Independence Structure of Natural Conjugate Densities to Exponential Families and the Gibbs Sampler," Scandinavian Journal of Statistics, 27, 111-127. [145]
30. Rajaratnam, B., Massam, H., and Carvalho, C. M. (2008), "Flexible Covariance Estimation in Graphical Gaussian Models," The Annals of Statistics, 36, 2818-2849. [141,151,152]
31. Roverato, A. (2002), "Hyper Inverse Wishart Distribution for Non-Decomposable Graphs and Its Application to Bayesian Inference for Gaussian Graphical Models," Scandinavian Journal of Statistics, 29, 391-411. [141-143,145,150]
32. Scott, J. G., and Berger, J. O. (2006), "An Exploration of Aspects of Bayesian Multiple Testing," Journal of Statististical Planing and Inference, 136, 2144-2162. [147] (Pubitemid 43380514)
33. Scott, J. G., and Carvalho, C. M. (2008), "Feature-Inclusion Stochastic Search for Gaussian Graphical Models," Journal of Computational and Graphical Statistics, 17, 790-808. [141,147,148,154]
34. Shen, H., and Huang, J. Z. (2005), "Analysis of Call Center Arrival Data Using Singular Value Decomposition," Applied Stochastic Models in Business and Industry, 21, 251-263. [151] (Pubitemid 40892080)
35. Smith, M., and Kohn, R. (2002), "Bayesian Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, 87, 1141-1153. [141] (Pubitemid 36136572)
36. Speed, T. P., and Kiiveri, H. T. (1986), "Gaussian Markov Distributions Over Finite Graphs," The Annals of Statistics, 14, 138-150. [141,143,144]
37. Tierney, L., and Kadane, J. (1986), "Accurate Approximations for Posterior Moments and Marginal Densities," Journal of the American Statistical Association, 81, 82-86. [145]
38. Wermuth, N. (1976), "Analogies Between Multiplicative Models in Contingency Tables and Covariance Selection," Biometrics, 32, 95-108. [140]
39. Wong, F., Carter, C. K., and Kohn, R. (2003), "Efficient Estimation of Covariance SelectionModels," Biometrika, 90, 809-830. [141,147] (Pubitemid 39047121)
40. Yang, R., and Berger, J. O. (1994), "Estimation of a Covariance Matrix Using the Reference Prior," The Annals of Statistics, 22, 1195-1211. [140,141]
41. Yuan, M., and Lin, Y. (2007), "Model Selection and Estimation in the Gaussian Graphical Model," Biometrika, 94, 19-35. [140] (Pubitemid 46410725)