Abstract
Markov chain Monte Carlo (MCMC) implementations of Bayesian inference for latent spatial Gaussian models are very computationally intensive, and restrictions on storage and computation time are limiting their application to large problems. Here we propose various parallel MCMC algorithms for such models. The algorithms' performance is discussed with respect to a simulation study, which demonstrates the increase in speed with which the algorithms explore the posterior distribution as a function of the number of processors. We also discuss how feasible problem size is increased by use of these algorithms.
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Blackford L.S., Ghol J., Cleary A.E., D"Azevedo E., Demmel J., Dhillon I., Dongarra J., Hammarling S., Henry G., Petitet A., Stanley K., Walker D., and Whaley R.C. 1997.ScaLAPACK Users" Guide, Society for Industrial & Applied Mathematics, Philadelphia.
Bradford R. and Thomas A. 1996. Markov chain Monte Carlo methods for family trees using parallel processor. Statistics and Computing 6: 67–75.
Cressie, N. 1993. Statistics for Spatial Data, 2nd edition. Wiley, New York.
Cybenko G. and Allen T.G. 1991. Multidimensional binary partitions: Distributed data structures for spatial partitioning. International Journal of Control 54: 1335–1352.
Diggle P.J., Tawn J.A., and Moyeed R.A. 1998. Model-based geostatistics (with discussion). Applied Statistics 47: 299–350.
Duff I.S. and van der Vorst H.A. 1999. Developments and trends in the parallel solution of linear systems. Parallel Computing 25: 1931–1970.
Gallivan K.A., Plemmons R.J., and Sameh A.H. 1990. Parallel algorithms for dense linear algebra computations. SIAM Review 32: 54–135.
Geyer C.J. and Thompson E.A. 1995. Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Amer. Statist. Assoc. 90: 909–920.
Heath M.T., Ng E., and Peyton B.W. 1991. Parallel algorithms for sparse linear systems. SIAM Review 33: 420–460.
Matérn B. 1960. Spatial Variation, 2nd edition. Springer-Verlag, New York.
Neal R.M. 2002. Circularly-coupled Markov chain sampling, Technical Report 9910 (revised), Department of Statistics, University of Toronto.
Robles Sánchez O.D. and Wilson S.P. 2002. Aset partitioning algorithm for use with a parallel approach to MCMC for latent Gaussian spatial models. Technical Report 02/01, Department of Statistics, Trinity College Dublin.
Rosenthal J. 2000. Parallel computing and Monte Carlo algorithms. Far East J. Theor. Stat. 4: 207–236.
Rue H. 2001. Fast sampling of Gaussian Markov random fields. Journal of the Royal Statistical Society B. 63: 325–338.
Rue H. and Tjelmeland H. 2002. Fitting Gaussian Markov random fields to Gaussian fields. Scandanavian Journal of Statistics 29: 30–48.
Schervish M.J. 1988. Applications of parallel computation to statistical inference. Journal of the American Statistical Associsation 83: 976–983.
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Whiley, M., Wilson, S.P. Parallel algorithms for Markov chain Monte Carlo methods in latent spatial Gaussian models. Statistics and Computing 14, 171–179 (2004). https://doi.org/10.1023/B:STCO.0000035299.51541.5e
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DOI: https://doi.org/10.1023/B:STCO.0000035299.51541.5e