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spam: A Sparse Matrix R Package with Emphasis on MCMC Methods for Gaussian Markov Random Fields

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  • Furrer, Reinhard
  • Sain, Stephan R.

Abstract

spam is an R package for sparse matrix algebra with emphasis on a Cholesky factorization of sparse positive definite matrices. The implemantation of spam is based on the competing philosophical maxims to be competitively fast compared to existing tools and to be easy to use, modify and extend. The first is addressed by using fast Fortran routines and the second by assuring S3 and S4 compatibility. One of the features of spam is to exploit the algorithmic steps of the Cholesky factorization and hence to perform only a fraction of the workload when factorizing matrices with the same sparsity structure. Simulations show that exploiting this break-down of the factorization results in a speed-up of about a factor 5 and memory savings of about a factor 10 for large matrices and slightly smaller factors for huge matrices. The article is motivated with Markov chain Monte Carlo methods for Gaussian Markov random fields, but many other statistical applications are mentioned that profit from an efficient Cholesky factorization as well.

Suggested Citation

  • Furrer, Reinhard & Sain, Stephan R., 2010. "spam: A Sparse Matrix R Package with Emphasis on MCMC Methods for Gaussian Markov Random Fields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i10).
    • Handle: RePEc:jss:jstsof:v:036:i10
    DOI: http://hdl.handle.net/10.18637/jss.v036.i10
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    Citations

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    Cited by:

    1. Roman Flury & Reinhard Furrer, 2021. "Discussion on Competition for Spatial Statistics for Large Datasets," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 599-603, December.
    2. Millo, Giovanni, 2014. "Maximum likelihood estimation of spatially and serially correlated panels with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 914-933.
    3. Ying C. MacNab, 2018. "Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 497-541, September.
    4. Gerber, Florian & Furrer, Reinhard, 2015. "Pitfalls in the Implementation of Bayesian Hierarchical Modeling of Areal Count Data: An Illustration Using BYM and Leroux Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(c01).
    5. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    6. Davies, Tilman M. & Bryant, David, 2013. "On Circulant Embedding for Gaussian Random Fields in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i09).
    7. Lee, Duncan, 2013. "CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i13).
    8. M. Bevilacqua & A. Fassò & C. Gaetan & E. Porcu & D. Velandia, 2016. "Covariance tapering for multivariate Gaussian random fields estimation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(1), pages 21-37, March.
    9. Padoan, Simone A. & Bevilacqua, Moreno, 2015. "Analysis of Random Fields Using CompRandFld," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i09).
    10. Toshihiro Hirano & Yoshihiro Yajima, 2013. "Covariance tapering for prediction of large spatial data sets in transformed random fields," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 913-939, October.
    11. Bevilacqua, Moreno & Caamaño-Carrillo, Christian & Porcu, Emilio, 2022. "Unifying compactly supported and Matérn covariance functions in spatial statistics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Schlather, Martin & Malinowski, Alexander & Menck, Peter J. & Oesting, Marco & Strokorb, Kirstin, 2015. "Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i08).
    13. Matthew J. Heaton & Abhirup Datta & Andrew O. Finley & Reinhard Furrer & Joseph Guinness & Rajarshi Guhaniyogi & Florian Gerber & Robert B. Gramacy & Dorit Hammerling & Matthias Katzfuss & Finn Lindgr, 2019. "A Case Study Competition Among Methods for Analyzing Large Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 398-425, September.
    14. Corentin M Barbu & Andrew Hong & Jennifer M Manne & Dylan S Small & Javier E Quintanilla Calderón & Karthik Sethuraman & Víctor Quispe-Machaca & Jenny Ancca-Juárez & Juan G Cornejo del Carpio & Fernan, 2013. "The Effects of City Streets on an Urban Disease Vector," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-9, January.
    15. Furrer, Reinhard & Bachoc, François & Du, Juan, 2016. "Asymptotic properties of multivariate tapering for estimation and prediction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 177-191.

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