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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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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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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