A diffusion-based spatio-temporal extension of Gaussian Matérn fields : (invited article with discussion)
Lindgren, Finn (University of Edinburgh (Escòcia))
Bakka, Haakon (Kontali (Noruega))
Bolin, David (King Abdullah University of Science and Technology (Aràbia Saudí))
Krainski, Elias (King Abdullah University of Science and Technology (Aràbia Saudí))
Rue, Håvard (King Abdullah University of Science and Technology (Aràbia Saudí))

Date:	2024
Abstract:	Gaussian random fields with Matérn covariance functions are popular models in spatial statistics and machine learning. In this work, we develop a spatio-temporal extension of the Gaussian Matérn fields formulated as solutions to a stochastic partial differential equation. The spatially stationary subset of the models have marginal spatial Matérn covariances, and the model also extends to Whittle-Matérn fields on curved manifolds, and to more general non-stationary fields. In addition to the parameters of the spatial dependence (variance, smoothness, and practical correlation range) it additionally has parameters controlling the practical correlation range in time, the smoothness in time, and the type of non-separability of the spatio-temporal covariance. Through the separability parameter, the model also allows for separable covariance functions. We provide a sparse representation based on a finite element approximation, that is well suited for statistical inference and which is implemented in the R-INLA software. The flexibility of the model is illustrated in an application to spatio-temporal modeling of global temperature data.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Stochastic partial differential equations ; Diffusion ; Gaussian fields ; Non-separable space-time models ; INLA ; Finite element methods
Published in:	SORT : statistics and operations research transactions, Vol. 48 Núm. 1 (2024) , p. 3-66 (Invited article) , ISSN 2013-8830

Adreça original: https://raco.cat/index.php/SORT/article/view/428665
DOI: 10.57645/20.8080.02.13

64 p, 15.3 MB

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