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Lookup NU author(s): Professor Emilio Porcu, Professor Chris Oates
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© Institute of Mathematical Statistics, 2024The Matérn model has been a cornerstone of spatial statistics for more than half a century. More recently, the Matérn model has been exploited in disciplines as diverse as numerical analysis, approximation theory, computational statistics, machine learning, and probability theory. In this article, we take a Matérn-based journey across these disciplines. First, we reflect on the importance of the Matérn model for estimation and prediction in spatial statistics, establishing also connections to other disciplines in which the Matérn model has been influential. Then, we position the Matérn model within the literature on big data and scalable computation: the SPDE approach, the Vecchia likelihood approximation, and recent applications in Bayesian computation are all discussed. Finally, we review recent devlopments, including flexible alternatives to the Matérn model, whose performance we compare in terms of estimation, prediction, screening effect, computation, and Sobolev regularity properties.
Author(s): Porcu E, Bevilacqua M, Schaback R, Oates CJ
Publication type: Article
Publication status: Published
Journal: Statistical Science
Year: 2024
Volume: 39
Issue: 3
Pages: 469-492
Print publication date: 01/08/2024
Online publication date: 28/06/2024
Acceptance date: 02/04/2018
ISSN (print): 0883-4237
ISSN (electronic): 2168-8745
Publisher: Institute of Mathematical Statistics
URL: https://doi.org/10.1214/24-STS923
DOI: 10.1214/24-STS923
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