Compactly Supported Correlation Functions

By Tilmann Gneiting. 2002

321 citations recorded by the source corpus.

Subfields: Ecology, Environmental Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/de0be2874b22b211869ddfb5c835359ed6426f34

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In Ecology

In Environmental Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Gaussian Processes for Prediction Technical Report PARG-0701 (2007, background): “The difficulty with parameterising such a function is due to the requirement thatK be positive semi-definite; regardless, many choices exist [Abrahamsen, 1997, Gibbs, 1997, Gneiting, 2002].”
On fixed-domain asymptotics and covariance tapering in Gaussian random field models (2011, background): “MR2291261 [7] Gneiting, T. (2002).”
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).”
Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets (2008, methodology): “If we have reason to believe that distant pairs of observations are independent, then we can model this structure using a compactly supported covariance function (Gneiting 2002).”
Classes of compactly supported covariance functions for multivariate random fields (2015, background): “The Turning Bands operator (Matheron 1963) offers a way of constructing such covariance models (Gneiting 2002).”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, methodology): “, vT K̃nnv ≥ 0 ∀v ∈ Rn [15], [50]–[52].”
Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry (2007, methodology): “Gneiting (2002b) reviews parametric models of compactly supported, stationary and isotropic covariance functions in a spatial setting.”
Separable approximations of space‐time covariance matrices (2007, methodology): “We consider a covariance model used by Gneiting et al. (2007) in a study of Irish wind speed. The data consists of time series of 6574 daily average wind speed recorded during the period 1961–1978 at n = 11 meteorological stations. The structure of the records is poor in space but rich in time, with”
Statistical Properties of Covariance Tapers (2013, background): “The two we examine here are the Wendland1 (W1) (Wendland 1995; Furrer, Genton, and Nychka 2006) and Bohman (B) (Bohman 1960; Gneiting 2002) tapers.”
Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics (2016, methodology): “As noted by Gneiting (2002a), GW and Matérn functions exhibit the same behavior at the origin, with the smoothness parameters of the two covariance models related by the equation ν = κ+ 1/2. Fourier transforms of radial versions of members of Φd, for a given d, have a simple expression, as reported ”
The Design and Analysis of Computer Experiments (2003, background): “Another useful compactly supported correlation function is the Bohman correlation function (Gneiting (2002)).”
Classes of Kernels for Machine Learning: A Statistics Perspective (2002, background): “Cressie and Huang (1999) and Gneiting (2002b) use (10) to derive nonseparable space-time stationary kernels, see also Christakos (2000) for illustrative examples.”
History and trends in solar irradiance and PV power forecasting: A preliminary assessment and review using text mining (2018, background): “The hole effect model (Gneiting, 2002) has been known for a long time in the geostatistics community.”
A full scale approximation of covariance functions for large spatial data sets (2012, methodology): “If we believe that distant pairs of observations are uncorrelated, then we can use a compactly supported covariance function to model the spatial dependence (Gneiting, 2002).”
Covariance Tapering for Interpolation of Large Spatial Datasets (2006, background): “Wu (1995), Wendland (1995, 1998), Gaspari and Cohn (1999), and Gneiting (2002) gave several procedures to construct compactly supported covariance functions with arbitrary degree of differentiability at the origin and at the support length.”
Strictly and non-strictly positive definite functions on spheres (2011, background): “Table 3 shows compactly supported families within the class 3 that have been introduced and studied by Wendland (1995) and Gneiting (1999a, 2002).”