The Matérn Model: A Journey Through Statistics, Numerical Analysis and Machine Learning

Emilio Porcu, Moreno Bevilacqua, Robert Schaback, Chris J. Oates

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

2 Citas (Scopus)

Resumen

The 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.

Idioma originalInglés
Páginas (desde-hasta)469-492
Número de páginas24
PublicaciónStatistical Science
Volumen39
N.º3
DOI
EstadoPublicada - 2024
Publicado de forma externa

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