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Fast sampling from a Gaussian Markov random field using Krylov subspace approaches

Simpson, Daniel P., Turner, Ian W., & Pettitt, Anthony N. (2008) Fast sampling from a Gaussian Markov random field using Krylov subspace approaches. [Working Paper] (Unpublished)

Abstract

Many applications in spatial statistics, geostatistics and image analysis require efficient techniques for sampling from large Gaussian Markov random fields (GMRFs). A suite of methods, based on the Cholesky decomposition, for sampling from GMRFs, sampling conditioned on a set of linear constraints, and computing the likelihood were presented by Rue (2001). In this paper, we present an alternate set of methods based on Krylov subspace approaches. These methods have the advantage of requiring far less storage than the Cholesky decomposition and may be useful in problems where computing a Cholesky decomposition is infeasible.

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ID Code: 14376
Item Type: Working Paper
Additional Information: Submitted to Scandinavian Journal of Statistics in 2008.
Keywords: Gaussian Markov random field, Lanczos decomposition, matrix functions, inverse square root, saddle point system
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2008 (The authors)
Deposited On: 14 Aug 2008
Last Modified: 08 Jul 2014 12:12

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