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Optimal design for prediction in random field models via covariance kernel expansions

Gauthier, Bertrand ORCID: and Pronzato, Luc 2016. Optimal design for prediction in random field models via covariance kernel expansions. Kunert, J., Muller, C. H. and Atkinson, A. C., eds. mODa 11 - Advances in Model-Oriented Design and Analysis: Proceedings of the 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016, Springer, pp. 103-111. (10.1007/978-3-319-31266-8_13)

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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 predictor, 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.

Item Type: Book Section
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISBN: 9783319312644
ISSN: 14311968
Last Modified: 02 Nov 2022 10:13

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