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Construction of Covariance Functions and Unconditional Simulation of Random Fields

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Advances and Challenges in Space-time Modelling of Natural Events

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 207))

Abstract

Covariance functions and variograms are the most important ingredients in the classical approaches to geostatistics. We give an overview over the approaches how models can be obtained. Variant types of scale mixtures turn out to be the most important way of construction. Some of the approaches are closely related to simulation methods of unconditional Gaussian random field, for instance the turning bands and the random coins. We discuss these methods and complement them by an overview over further methods.

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Acknowledgements

The author is grateful to Sebastian Engelke, Alexander Malinowski, Marco Oesting, Robert Schaback, and Kirstin Strokorb for valuable hints and comments.

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  1. Centre for Statistics, Georg-August-Universität Göttingen, Goldschmidtstr. 7, D – 37077, Gottingen, Germany

    Martin Schlather

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  1. Martin Schlather
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Editors and Affiliations

  1. Facultad de Derecho y Ciencias Sociales, Área de Estadística, Universidad de Castilla la Mancha, Avenida Camilo Jose Cela 14, Ciudad Real, 13005, Spain

    Emilio Porcu

  2. , Statistics, Universidad de Castilla la Mancha, Cobertizo San Pedro Martir, Toledo, 45071, Spain

    José–María Montero

  3. , Mathematics Stochastics, Universität Göttingen, Goldschmidtstrasse 7, Göttingen, 37077, Germany

    Martin Schlather

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Schlather, M. (2012). Construction of Covariance Functions and Unconditional Simulation of Random Fields. In: Porcu, E., Montero, J., Schlather, M. (eds) Advances and Challenges in Space-time Modelling of Natural Events. Lecture Notes in Statistics(), vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17086-7_2

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