Spam: A sparse matrix R package with emphasis on MCMC methods for gaussian markov random fields

Journal of Statistical Software

Volumn 36, Issue 10, 2010, Pages 1-25

  Furrer, Reinhard ^a   Sain, Stephan R ^b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Cholesky factorization; Compactly supported covariance function; Compressed sparse row format; S3 S4; Stochastic modeling; Symmetric positive definite matrix

Indexed keywords

EID: 77958198415     PISSN: 15487660     EISSN: 15487660     Source Type: Journal    
DOI: 10.18637/jss.v036.i10     Document Type: Article

References (33)

1. Bates D, Maechler M (2010). Matrix: Sparse and Dense Matrix Classes and Methods. R package version 0.999375-42, URL http://CRAN.R-project.org/package=Matrix.
2. Becker RA, Wilks AR, Brownrigg R, Minka TP (2010). maps: Draw Geographical Maps. R package version 2.1-4, URL http://CRAN.R-project.org/package=maps.
3. Besag J (1974). "Spatial Interaction and the Statistical Analysis of Lattice Systems." Journal of the Royal Statistical Society B, 36(2), 192-225.
4. Besag J, York J, Mollíe A (1991). "Bayesian Image Restoration, with Two Applications in Spatial Statistics." Annals of the Institute of Statistical Mathematics, 43, 1-59.
5. Chambers JM (1998). Programming with Data: A Guide to the S Language. Springer-Verlag, Secaucus, NJ, USA.
6. Davis TA (2004). "Algorithm 832: UMFPACK V4.3-An Unsymmetric-Pattern Mul-tifrontal Method." ACM Transactions on Mathematical Software, 30(2), 196-199. doi:10.1145/992200.992206.
7. Duff IS, Erisman AM, Reid JK (1986). Direct Methods for Sparse Matrices. Oxford University Press, New York, NY, USA.
8. Furrer R, Genton MG, Nychka D (2006). "Covariance Tapering for Interpolation of Large Spatial Datasets." Journal of Computational and Graphical Statistics, 15(3), 502-523.
9. Furrer R, Nychka D, Sain S (2009). fields: Tools for Spatial Data. R package version 6.01, URL http://CRAN.R-project.org/package=fields.
10. George A, Liu JWH (1981). Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall Inc., Englewood Cliffs, N. J. Prentice-Hall Series in Computational Mathematics.
11. George JA (1971). Computer Implementation of the Finite Element Method. Ph.D. thesis, Stanford University, Stanford, CA, USA.
12. Gilbert JR, Ng EG, Peyton BW (1994). "An Efficient Algorithm to Compute Row and Column Counts for Sparse Cholesky Factorization." SIAM Journal on Matrix Analysis and Applications, 15(4), 1075-1091. doi:10.1137/S0895479892236921.
13. Gould NIM, Hu Y, Scott JA (2005a). Complete Results for a Numerical Evaluation of Sparse Direct Solvers for the Solution of Large, Sparse, Symmetric Linear Systems of Equations. Numerical Analysis Internal Report 2005-1 (revision 2). Rutherford Appleton Laboratory. Available from http://www.numerical.rl.ac.uk/reports/reports.shtml.
14. Gould NIM, Hu Y, Scott JA (2005b). "A Numerical Evaluation of Sparse Direct Symmetric Solvers for the Solution of Large Sparse, Symmetric Linear Systems of Equations." Technical report, RAL-TR-2005-005. Rutherford Appleton Laboratory. Available from http://www.numerical.rl.ac.uk/reports/reports.shtml.
15. Held L, Natario I, Fenton S, Rue H, Becker N (2005). "Towards Joint Disease Mapping." Statistical Methods in Medical Research, 14(1), 61-82.
16. Ihaka R, Gentleman R (1996). "R: A Language for Data Analysis and Graphics." Journal of Computational and Graphical Statistics, 5(3), 299-314.
17. Knorr-Held L, Raßer G (2000). "Bayesian Detection of Clusters and Discontinuities in Disease Maps." Biometrics, 56(1), 13-21.
18. Knorr-Held L, Rue H (2002). "On Block Updating in Markov Random Models for Disease Mapping." Scandinavian Journal of Statistics, 29(4), 597-614.
19. Koenker R, Ng P (2010). SparseM: Sparse Linear Algebra. R package version 0.85, URL http://CRAN.R-project.org/package=SparseM.
20. Liu JWH (1985). Modification of the Minimum-Degree Algorithm by Multi-
21. ple Elimination." ACM Transactions on Mathematical Software, 11(2), 141-153. doi:10.1145/214392.214398.
22. Liu JWH (1992)."The Multifrontal Method for Sparse Matrix Solution: Theory and Practice." SIAM Review, 34(1), 82-109. doi:10.1137/1034004.
23. Liu JWH, Ng EG, Peyton BW (1993). "On Finding Supernodes for Sparse Matrix Computations." SIAM Journal on Matrix Analysis and Applications, 14(1), 242-252. doi:10.1137/0614019.
24. Lumley T (2004). Programmers' Niche: A Simple Class, in S3 and S4." R News, 4(1), 33-36. URL http://CRAN.R-project.org/doc/Rnews/.
25. Mollié A (1996). "Bayesian Mapping of Disease." In WR Gilks, S Richardson, DJ Spiegelhalter (eds.), Markov Chain Monte Carlo in Practice, pp. 359-379. Chapman & Hall, London.
26. Ng EG, Peyton BW (1993a). "Block Sparse Cholesky Algorithms on Advanced Uniprocessor Computers." SIAM Journal on Scientific Computing, 14(5), 1034-1056. doi:10.1137/0914063.
27. Ng EG, Peyton BW (1993b). "A Supernodal Cholesky Factorization Algorithm for Shared-Memory Multiprocessors." SIAM Journal on Scientific Computing, 14(4), 761-769. doi:10.1137/0914048.
28. R Development Core Team (2010a). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/.
29. R Development Core Team (2010b). Writing R Extensions. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-11-9, URL http://www.R-project.org/.
30. Rue H, Held L (2005). Gaussian Markov Random Fields: Theory and Applications. Chapman & Hall, London
31. Saad Y (1994). SPARSKIT: A Basic Tool Kit for Sparse Matrix Computations. Available at http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html.
32. Sherman AH (1975). On the Efficient Solution of Sparse Systems of Linear and Nonlinear Equations. Ph.D. thesis, Yale University, New Haven, CT, USA.
33. The MathWorks, Inc (2007). MATLAB - The Language of Technical Computing, Version 7.5. The MathWorks, Inc., Natick, Massachusetts. URL http://www.mathworks.com/products/matlab/.