Geostatistics: Modeling Spatial Uncertainty

By Li Zheng. 2001

376 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/1eef118dd1ad005f5e9d6561b09bb1b6599c4fad

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Citations in the corpus

Calculations of Sobol indices for the Gaussian process metamodel (2008, neutral): “To simplify the notations, the conditional Gp ( Y | Y s , X s , β , σ, θ , p ) will now be written in a simpliﬁed form: Y Gp | Y s ,X s ( X, ω ).”
Sequential design of computer experiments for the estimation of a probability of failure (2010, methodology): “…again a linear combination of the observations, as in (7), and the weights λi(x;xn) are again solutions of a system of linear equations (see, e.g., Chilès and Delfiner, 1999), which can be written under a matrix form as ( k(xn, xn) h(xn) T h(xn) 0 )( λ(x;xn) µ(x) ) = ( k(x, xn) h(x) ) ,…”
Maximum‐likelihood estimation for multivariate spatial linear coregionalization models (2007, positive): “This covariogram corresponds to the linear coregionalization model (Chilés and Delfiner, 1999, Subsection 5.6.5; Wackernagel, 1998, Chapter 26): YðsÞ ¼ mðsÞ þ X K k¼0 X k ðsÞ (3) where X 0 (s) is a stationary but uncorrelated p-variate process with mean 0, that is, EX 0 ðsÞ ¼ 0; CovðX 0 ðsÞ; X 0 ðs…”
A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space (2013, methodology): “A Universal Kriging predictor for functional data 2213 Function (7) has the same properties as its finite-dimensional analogue (Chilès and Delfiner, 1999); in particular it is a conditionally negative definite function: ∑ i ∑ j λiλjγ(si, sj) ≤ 0, ∀ si, sj ,∈ D, ∀ λi, λj ∈ R s.”
Approximating likelihoods for large spatial data sets (2004, methodology): “Since variograms must be conditionally negative definite (Chilès and Delfiner, 1999), practical variogram estimation generally requires the selection of some parametric class of variograms and the estimation of these parameters, although nonparametric methods using spectral approximations are availa”
Verification and Validation in Computational Fluid Dynamics (2002, background): “For example, in a complex physical process how do you determine ‘‘how nearby’’ is the prediction case from cases in the validation database? Struggling with the strength or quantification of the inference in a prediction is presently an important topic of research [66].”
Estimating deformations of isotropic Gaussian random fields on the plane (2008, neutral): “07 23 v1 [ m at h. ST ] 4 A pr 2 00 8 The Annals of Statistics 2008, Vol. 36, No. 2, 719–741 DOI: 10.1214/009053607000000893 c© Institute of Mathematical Statistics, 2008”
Covariance Tapering for Interpolation of Large Spatial Datasets (2006, neutral): “Some scientific applications require that the station data be interpolated to a fine grid, and we assume a prediction grid with a spacing of approximately 4 km.”
A generic framework for spatial prediction of soil variables based on regression-kriging (2004, background): “The term Kriging with external drift (further referred to as KED) is more commonly used when the drift is defined 'externally' through some auxiliary variables (Chiles and Delfiner, 1999; Wackernagel, 1998).”
On the consistent separation of scale and variance for Gaussian random fields (2009, background): “In this case, it is common to consider a class of covariance structures indexed by a finite number of parameters which are then estimated from the observations (see [12] or [9] for an introduction to spatial statistical techniques).”
Prediction of spatial soil property information from ancillary sensor data using ordinary linear regression: Model derivations, residual assumptions and model validation tests (2008, methodology): “…and disjunctive kriging are two commonly used modeling techniques for estimating such probabilities (Matheron, 1976; Deutsch and Journel, 1992; Chilès and Delfiner, 1999; Webster and Oliver, 2001); note that cokriging equivalent forms of these techniques are sometimes used when ancillary…”
A chronology of interpolation: from ancient astronomy to modern signal and image processing (2002, background): “Kriging has been studied in the context of geostatistics [312], [314], [315], cartography [316], and meteorology [317] and is closely related to interpolation by thin-plate splines or radial basis functions [318], [319].”
Multiple-point geostatistical modeling based on the cross-correlation functions (2012, background): “They are based on defining an array of points or pixels in a regular grid [11, 18, 27], with the pixels representing various properties of a reservoir.”