Fast and Exact Simulation of Large Gaussian Lattice Systems in R2: Exploring the Limits
Authors: Gneiting, Tilmann1; Ševčíková, Hana1; Percival, Donald B.2; Schlather, Martin3; Jiang, Yindeng1
Source: Journal of Computational & Graphical Statistics, Volume 15, Number 3, September 2006 , pp. 483-501(19)
Publisher: American Statistical Association
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Abstract:
The circulant embedding technique allows for the fast and exact simulation of stationary and intrinsically stationary Gaussian random fields. The method uses periodic embeddings and relies on the fast Fourier transform. However, exact simulations require that the periodic embedding is nonnegative definite, which is frequently not the case for two-dimensional simulations. This work considers a suggestion by Michael Stein, who proposed nonnegative definite periodic embeddings based on suitably modified, compactly supported covariance functions. Theoretical support is given to this proposal, and software for its implementation is provided. The method yields exact simulations of planar Gaussian lattice systems with 106 and more lattice points for wide classes of processes, including those with powered exponential, Matérn, and Cauchy covariances.Keywords: CIRCULANT EMBEDDING; COMPACTLY SUPPORTED CORRELATION FUNCTION; CUT-OFF EMBEDDING; FAST FOURIER TRANSFORM; GAUSSIAN RANDOM FUNCTION; INTRINSIC EMBEDDING; TORUS PROCESS
Document Type: Research article
DOI: 10.1198/106186006X128551
Affiliations: 1: Department of Statistics, University of Washington, Box 354322, Seattle, WA 98195-4322 2: Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA 98195-5640 3: Helmut-Schmidt-Universität, Institut für Statistik und Quantitative Ökonomik, Postfach 700822, 22008 Hamburg, Germany
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