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Fast and exact simulation of univariate and bivariate Gaussian random fields
Author(s) -
Moreva Olga,
Schlather Martin
Publication year - 2018
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.188
Subject(s) - univariate , bivariate analysis , covariance , covariance function , circulant matrix , random field , gaussian , mathematics , gaussian random field , covariance mapping , random function , embedding , matérn covariance function , exponential function , gaussian process , random variate , random variable , algorithm , statistics , mathematical analysis , computer science , covariance intersection , multivariate statistics , physics , artificial intelligence , quantum mechanics
Circulant embedding is a powerful algorithm for fast simulation of stationary Gaussian random fields on a rectangular grid in R n , which works perfectly for compactly supported covariance functions. Cut‐off circulant embedding techniques have been developed for univariate random fields for dimensions up to R 3 and rely on the modification of a covariance function outside the simulation window, such that the modified covariance function is compactly supported. In this paper, we propose extensions of the cut‐off approach for univariate and bivariate Gaussian random fields. In particular, we provide a method for simulating bivariate fields with a powered exponential model and the Matérn model for certain sets of parameters. Copyright © 2018 John Wiley & Sons, Ltd.