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Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)



Gaussian random fields: with and without covariances

Authors: N. H. Bingham and Tasmin L. Symons
Journal: Theor. Probability and Math. Statist. 106 (2022), 27-40
MSC (2020): Primary 54C40, 14E20; Secondary 46E25, 20C20
Published electronically: May 16, 2022
MathSciNet review: 4438442
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Abstract | References | Similar Articles | Additional Information

Abstract: We begin with isotropic Gaussian random fields, and show how the Bochner–Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Matérn processes on Euclidean space, spheres, manifolds and graphs, using Bessel potentials and stochastic partial differential equations (SPDEs). We then turn from this continuous setting to approximating discrete settings, Gaussian Markov random fields (GMRFs), and the computational advantages they bring in handling large data sets, by exploiting the sparseness properties of the relevant precision (concentration) matrices.

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Additional Information

N. H. Bingham
Affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

Tasmin L. Symons
Affiliation: Telethon Kids Institute, 15 Hospital Avenue, Perth, WA 6009, Australia

Keywords: Gaussian random field, covariance function, Bessel potential, stochastic partial differential equation, Matérn process, Gaussian Markov random field, precision matrix, sparseness, numerical linear algebra
Received by editor(s): August 4, 2021
Accepted for publication: October 18, 2021
Published electronically: May 16, 2022
Dedicated: To the memory of Mikhailo Iosifovich Yadrenko, on his 90th birthday
Article copyright: © Copyright 2022 Taras Shevchenko National University of Kyiv