Studies in the history of probability and statistics XLIX On the Matérn correlation family

By Peter Guttorp, Tilmann Gneiting. 2006

307 citations recorded by the source corpus.

Subfields: Applied Mathematics, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e258958a57dbe7b59194f8dc2cb6187a6eae5042

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Citations in the corpus

Spatial and spatio-temporal models with R-INLA. (2013, unknown): “In fact, as described in Guttorp and Gneiting (2006), the Mat`ern family is a very ﬂexible class of covariance functions able to cover a wide range of spatial ﬁelds.”
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (2011, background): “The Matérn covariance function appears naturally in various scientific fields (Guttorp and Gneiting, 2006), but the important relationship that we shall make use of is that a GF x.”
Strictly and non-strictly positive definite functions on spheres (2011, background): “Table 2 shows some well known parametric families within the class ∞, namely the powered exponential family (Yaglom, 1987), the Matérn class (Guttorp and Gneiting, 2006), the generalized Cauchy family (Gneiting and Schlather, 2004), and the Dagum class (Berg, Mateu and Porcu, 2008), along with the…”
Matérn Cross-Covariance Functions for Multivariate Random Fields (2010, methodology): “A class of isotropic covariance functions that has received a great deal of attention recently is the Matérn family (Matérn 1986; Guttorp and Gneiting 2006), which specifies the covariance function as σ 2M(h|ν,a) where σ 2 > 0 is the marginal variance and M(h|ν,a) = 2 1−ν (ν) (a‖h‖)νKν(a‖h‖) (1) is…”
A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components (2012, background): “In the univariate setting, that is, when p =1, there are many available covariance models (Gneiting, Genton, and Guttorp 2007 ) but the Matern family (Matern 1960 ) has found widespread interest in recent years, perhaps due to its strong support from Stein ( 1999 ); see also Guttorp and Gneiting ”
Quasi-site-specific multivariate probability distribution model for sparse, incomplete, and three-dimensional spatially varying soil data (2021, unknown): “The two- parameter Whittle-Matérn (WM) model (Stein 1999; Guttorp and Gneiting 2006; Liu et al. 2017; Ching and Phoon 2019b; Wang et al. 2018) is adopted as the auto-correlation model: r(D) = 2 G(n) · p √ · G(n+ 0.5) · |D| G(n) · d ( )n Kn 2 p √ · G(n+ 0.5) · |D| G(n) · d ( ) (19) where ρ(Δ) is the…”
Estimation and prediction of the spatial occurrence of fish species using Bayesian latent Gaussian models (2013, methodology): “For more information on the Matérn covariance model see Handcock and Stein (1993); Stein (1999); Guttorp and Gneiting (2006).”
divand-1.0: n -dimensional variational data analysis for ocean observations (2013, background): “The correlation function is the class of the Matérn family of spatial correlations (Matérn, 1986; Guttorp and Gneiting, 2006; Weaver and Mirouze, 2013).”
Likelihood approximation with hierarchical matrices for large spatial datasets (2017, background): “The varied history of this family of models can be found in Guttorp and Gneiting (2006). The Matérn covariance depends only on the distance h := ∥s − s∥, where s and s are any two spatial locations.”