A sparse matrix approach to Bayesian computation in large linear models

Computational Statistics and Data Analysis

Volumn 44, Issue 3, 2004, Pages 493-516

  Wilkinson, Darren J ^a   Yeung, Stephen K H ^a  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

Bayes linear models; Block sampling; Gaussian models; Linear systems; Local computation; Markov chain Monte Carlo (MCMC); Multivariate normal; Precision matrix; Sparse matrices

Indexed keywords

ALGORITHMS; GRAPH THEORY; LINEAR EQUATIONS; MONTE CARLO METHODS;

BAYESIAN COMPUTATION;

COMPUTATIONAL METHODS;

STATISTICAL ANALYSIS;

EID: 0242286591     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(02)00252-9     Document Type: Article

References (26)

1. Boys R.J. Henderson D.A. Wilkinson D.J. Detecting homogeneous segments in DNA sequences by using hidden Markov models J. Roy. Statist. Soc. C 49 2 2000 269-285
2. Chib S. Marginal likelihood from the Gibbs output J. Amer. Statist. Assoc. 90 432 1995 1313-1321
3. Chib S. Calculating posterior distribution and modal estimates in Markov mixture models J. Econometrics 75 1996 79-97
4. Chib S. Carlin B.P. On MCMC sampling in hierarchical longitudinal models Statist. Comput. 9 1999 17-26
5. Cowell R.G. Dawid A.P. Lauritzen S.L. Speigelhalter D.J. Probabilistic Networks and Expert Systems 1999 Springer New York
6. Duff I.S. Erisman M. Reid J.K. Direct Methods for Sparse Matrices 1986 Oxford Science Publications Oxford
7. Gamerman, D., Moreira, A. R. B., Rue, H., 2000. Space-varying regression models: Specifications and simulations. Technical Report No. 4, Instituto de Pesquisa Econmica Aplicada, Rio de Janeiro, available at http://www.ipea.gov.br/ftp/wp/index.html.
8. Garća-Cortés L.A. Sorensen D. On a multivariate implementation of the Gibbs sampler Genetics Selection Evolut. 28 1996 121-126
9. Gelfand A.E. Sahu S.K. Carlin B.P. Efficient parametrisations for normal linear mixed models Biometrika 82 3 1995 479-488
10. George, A., Liu, J.W., 1981. Computer solution of Large Sparse Positive Definite Systems. Series in Computational Mathematics. Prentice-Hall, Englewood Cliffs, NJ.
11. Goldstein, M., 1999. Bayes linear analysis. In: S. Kotz, N.L. Johnson, C.B. Read (Eds.), Encyclopedia of Statistical Sciences, update vol. 3, Wiley, Chichester.
12. Goldstein M. Wilkinson D.J. Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics Statist. Comput. 10 4 2000 311-324
13. Golub G.H. Van Loan C.F. Matrix Computations 3rd Edition 1996 Johns Hopkins University Press Boltimore, MD
14. Hobert J.P. Geyer C.J. Geometric ergodicity of Gibbs and block Gibbs samplers for a hierarchical random effects model J. Multivariate Anal. 67 1998 414-430
15. Knorr-Held, L., Rue, H., 2002. On block updating in Markov random field models for disease mapping. Scand. J. Statist., to appear.
16. Kontoghiorghes E.J. Parallel Algorithms for Linear Models: Numerical Methods and Estimation Problems Advances in Computational Economics Vol. 15 2000 Kluwer Boston
17. Lauritzen S.L. Propagation of probabilities, means, and variances in mixed graphical association models J. Amer. Statist. Assoc. 87 420 1992 1098-1108
18. Lauritzen S.L. Graphical Models 1996 Oxford Science Publications Oxford
19. Liu J.S. Wong W.H. Kong A. Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes Biometrika 81 1994 27-40
20. Ripley B.D. Stochastic Simulation 1987 Wiley New York
21. Roberts G.O. Sahu S.K. Updating schemes, correlation structure, blocking and parameterisation for the Gibbs sampler J. Roy. Statist. Soc. B 59 2 1997 291-317
22. Rue H. Fast sampling of Gaussian Markov random fields J. Roy. Statist. Soc. B 63 2 2001 325-338
23. Tanner M.A. Wong W.H. The calculation of posterior distributions by data augmentation J. Amer. Statist. Assoc. 82 398 1987 528-540
24. Tierney L. Markov chains for exploring posterior distributions (with discussion) Ann. Statist. 21 1994 1701-1762
25. Wilkinson, D.J., 2001. GDAGsim 0.2 User Guide. Statistics Preprint STA01,1, University of Newcastle, available from http://www.staff.ncl.ac.uk/d.j.wilkinson/software/gdagsim/
26. Wilkinson D.J. Yeung S.K.H. Conditional simulation from highly structured Gaussian systems, with application to blocking-MCMC for the Bayesian analysis of very large linear models Statist. Comput. 12 2002 287-300