The intrinsic random functions and their applications

By G. Matheron. 1973

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Citations in the corpus

Spatial‐Process Estimates as Smoothers (2012, methodology): “This stochastic model has a rigorous foundation stemming from the work of Matheron (1973) on intrinsic random functions and the reader is referred to this work and Wahba (1990a) for the development of this theory.”
Changes in variance and correlation of soil properties with scale and location: analysis using an adapted maximal overlap discrete wavelet transform (2001, background): “Geostatisticians have discovered how to deal with a nonstationary mean using intrinsic random functions of order greater than 0 (irfk) and generalized covariances (Matheron, 1973) and by universal kriging (Matheron, 1969).”
A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models (2013, background): “The present paper focuses on Kriging metamodel [4] for its exact interpolation nature and its stochastic property which provides a measure of the prediction uncertainty.”
Recent developments on the construction of spatio-temporal covariance models (2008, methodology): “Starting from a univariate covariance C1(t) on the real line, Matheron (1973) suggested an effective way to construct an isotropic covariance on R d by the turning bands”
Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations (2003, background): “Note that kriging models are more generally concerned with intrinsic random functions (IRF) [113], generalisations of stationary processes which are also frequently used in the spline smoothing context.”
Efficient methods for large‐scale linear inversion using a geostatistical approach (2012, background): “For a more detailed discussion on covariance kernels that permissible, we refer the reader to the following references [Christakos, 1984; Matheron, 1973].”
Gaussian process dynamic programming (2009, background): “Matheron (1973) and others introduced Gaussian processes to geostatistics decades ago under the name kriging .”
Classes of Kernels for Machine Learning: A Statistics Perspective (2002, background): “Such kernels are referred to as generalized kernels ( Matheron , 1973 ) .”
Vector Random Fields with Second-Order Moments or Second-Order Increments (2011, background): “For a univariate random field with second-order increments, it is known that its variogram is conditionally negative definite [22].”
Why Experimenters Might Not Always Want to Randomize, and What They Could Do Instead (2016, background): “see Robert (2007). O’Hagan and Kingman (1978) considered Gaussian process priors in the context of experimental design, taking an approach similar to ours but without allowing for covariates.”
A new learning function for Kriging and its applications to solve reliability problems in engineering (2015, methodology): “Kriging, developed by Krige [21] and then developed by Matheron [22], is an exact interpolation method and a form of generalized linear regression for the formulation of an optimal estimator in a minimummean square error sense.”
Latin hypercube lattice sample selection strategy for correlated random hydraulic conductivity fields (2003, methodology): “D Gaussian simulation algorithm actually implemented [Deutsch and Journel, 1998; Mantoglou and Wilson, 1981; Matheron, 1973].”