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

Handcock & Stein (1993) introduced the Matern family of spatial correlations into statistics as a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field. We document the varied history of this family, which includes contributions by eminent physical scientists and statisticians. Copyright 2006, Oxford University Press.

[1]  Hermann Hankel.  Bestimmte Integrale mit Cylinderfunctionen , 1875 .

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[14]  S. Meier.  Planar geodetic covariance functions , 1981 .

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[17]  Thomas H. Jordan,et al.  Stochastic Modeling of Seafloor Morphology: Inversion of Sea Beam Data for Second-Order Statistics , 1988 .

[18]  John T. Kent,et al.  Continuity Properties for Random Fields , 1989 .

[19]  M. Stein,et al.  A Bayesian analysis of kriging , 1993 .

[20]  J. R. Wallis,et al.  An Approach to Statistical Spatial-Temporal Modeling of Meteorological Fields , 1994 .

[21]  John A. Goff,et al.  Modal fields: A new method for characterization of random seismic velocity heterogeneity , 1994 .

[22]  C. R. Dietrich,et al.  A Simple and Efficient Space Domain Implementation of the Turning Bands Method , 1995 .

[23]  Tilmann Gneiting,et al.  Closed Form Solutions of the Two-Dimensional Turning Bands Equation , 1998 .

[24]  S. Cohn,et al.  Ooce Note Series on Global Modeling and Data Assimilation Construction of Correlation Functions in Two and Three Dimensions and Convolution Covariance Functions , 2022 .

[25]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

[26]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[27]  Robert Piessens,et al.  The Hankel Transform , 2000 .

[28]  M. Fuentes.  Spectral methods for nonstationary spatial processes , 2002 .

[29]  Matthias W. Seeger,et al.  Gaussian Processes For Machine Learning , 2004, Int. J. Neural Syst..

[30]  Samuel Kotz,et al.  Multivariate T-Distributions and Their Applications , 2004 .

[31]  B. Minasny,et al.  The Matérn function as a general model for soil variograms , 2005 .