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1 ESAT-STADIUS - Center for Dynamical Systems, Signal Processing and Data Analytics 2 Laboratoire d-Informatique, Signaux, et Systèmes de Sophia-Antipolis I3S - Equipe SYSTEMES SIS - Signal, Images et Systèmes 3 GdR MASCOT-NUM - Méthodes d-Analyse Stochastique des Codes et Traitements Numériques

Abstract : We consider experimental design for the prediction of a realization of a second-order random field Z with known covariance function, or kernel, K. When the mean of Z is known, the integrated mean squared error of the best linear pre-dictor, approximated by spectral truncation, coincides with that obtained with a Bayesian linear model. The machinery of approximate design theory is then available to determine optimal design measures, from which exact designs collections of sites where to observe Z can be extracted. The situation is more complex in the presence of an unknown linear parametric trend, and we show how a Bayesian linear model especially adapted to the trend can be obtained via a suitable projection of Z which yields a reduction of K.

Keywords : random field model kernel reduction optimal design Bayesian linear model Karhunen-Loève expansion

Autor: Bertrand Gauthier - Luc Pronzato -

Fuente: https://hal.archives-ouvertes.fr/


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