Prediction by conditional simulation: models and algorithms

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.