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Intrinsic Kriging and prior information. (English) Zbl 1091.62098

Assume \(F(x)\) is a random process with zero mean which serves to model an output depending on a vector \(x\) of factors. Assume also that \(F(x)\in L^2(\Omega, {\mathcal A},P)\) for all \(x\). A Kriging estimator is the best linear approximation of \(F(x)\) in the space generated by random variables \(F(x_1),\dots, F(x_{n})\). The main idea of intrinsic Kriging is to assume that differences such as \(F(x)-F(y)\) are weakly stationary, whereas \(F(x)\) could be non-stationary. Intrinsic Kriging (viewed as a semi-parametric formulation of Kriging) can be used with an additional set of factors to take into account a specific type of prior information. The authors show that it is thus very easy to transform a black-box model into a grey-box one. The prediction error is orthogonal in some sense to the prior information that has been incorporated. An application to flow measurements is presented.

MSC:

62M99 Inference from stochastic processes
62G99 Nonparametric inference
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