Nonstationary spatial covariance functions

By Michael L. Stein. 2005

89 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c82805ac8b4f63bf32eee78feee636d6909044e8

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Citations in the corpus

An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (2011, background): “…function and there is a vast literature on this subject (Sampson and Guttorp, 1992; Higdon, 1998; Hughes-Oliver et al., 1998; Cressie and Huang, 1999; Higdon et al., 1999; Fuentes, 2001; Gneiting, 2002; Stein, 2005; Paciorek and Schervish, 2006; Jun and Stein, 2008; Yue and Speckman, 2010).”
Matérn Cross-Covariance Functions for Multivariate Random Fields (2010, background): “Extensions to nonstationary settings are available along the lines of Stein (2005) and Schlather (2010).”
A class of Matérn-like covariance functions for smooth processes on a sphere (2015, methodology): “We used the nonstationary Matérn covariance model that allows for spatially varying local dependence through ν (Stein, 2005; Paciorek and Schervish, 2006; Kleiber and Nychka, 2012).”
Second-order non-stationary modeling approaches for univariate geostatistical data (2017, background): “Stein (2005) shows how these two ideas can be combined to produce: (i) a Matérn non-stationary covariance function with spatially varying regularity parameter depicted by Eq.”
A non‐stationary covariance‐based Kriging method for metamodelling in engineering design (2007, background): “Other related works could be found in Schmidt and O’Hagan [13], Pintore and Holmes [22], and Stein [23].”
Some covariance models based on normal scale mixtures (2011, methodology): “Another classification is based on the construction principles (Ma (2008)), such as spectral methods (Stein (2005a)), multiplicative mixture models (Ma (2002)), additive models (Ma (2005c)), turning bands upgrade (Kolovos et al. (2004)), derivatives and integrals (Ma (2005b)), and Gneiting’s (2002)…”
Spatial modelling using a new class of nonstationary covariance functions (2006, background): “One could also use different values of ν, following Stein (2005), who has extended our approach to allow for spatially-varying ν.”