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Space, Structure and Randomness pp 39–68Cite as

Prediction by conditional simulation: models and algorithms

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Part of the book series: Lecture Notes in Statistics ((LNS,volume 183))

Abstract

Prediction here refers to the behavior of a regionalized variable: average ozone concentration in April 2004 in Paris, maximum lead concentration in an industrial site, recoverable reserves of an orebody, breakthrough time from a source of pollution to a target, etc. Dedicating a whole chapter of a book in honor to Georges Matheron to prediction by conditional simulation is somewhat paradoxical. Indeed performing simulations requires strong assumptions, whereas Matheron did his utmost to weaken the prerequisites for the prediction methods he developed. Accordingly, he never used them with the aim of predicting and they represented a marginal part of his activity. The turning bands method, for example, is presented very briefly in a technical report on the Radon transform to illustrate the one-to-one mapping between d-dimensional isotropic covariances and unidimensional covariances1 [44]. As for the technique of conditioning by kriging, it is nowhere to be found in Matheron’s entire published works, as he merely regarded it as an immediate consequence of the orthogonality of the kriging estimator and the kriging error.

Matheron submitted a paper on the turning bands method to the Advances in Applied Probability, which he later merged with another paper [46]. This project paper, available as [45], mainly focuses on the turning bands operator. It is worth noticing that Matérn [33] already had a similar attitude, presenting the principle of the turning bands in a few lines as an illustration of the relation between covariances in IR d and IR.

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Authors and Affiliations

  1. Centre de Géostatistique, Ecole Nationale Supérieure des Mines de Paris, 35 rue Saint Honoré, 77300, Fontainebleau, France

    Jean-Paul Chilès & Christian Lantuéjoul

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  1. Jean-Paul Chilès
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  1. Centre de Morphologie Mathématique, Ecole des Mines de Paris, 35 rue Saint Honoré, 77305, Fontainebleau, France

    Michel Bilodeau  & Fernand Meyer  & 

  2. Direction des recherches, Ecole des Mines de Paris, 60 Boulevard Saint Michel, 75272, Paris Cedex 06, France

    Michel Schmitt

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Chilès, JP., Lantuéjoul, C. (2005). Prediction by conditional simulation: models and algorithms. In: Bilodeau, M., Meyer, F., Schmitt, M. (eds) Space, Structure and Randomness. Lecture Notes in Statistics, vol 183. Springer, New York, NY. https://doi.org/10.1007/0-387-29115-6_3

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