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Optimal Design for Prediction in Random Field Models via Covariance Kernel Expansions

  • Bertrand GauthierEmail author
  • Luc Pronzato
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

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 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.

Keywords

Canonical Extension Best Linear Unbiased Predictor Integrate Mean Square Error Covariance Kernel Uncorrelated Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was partially supported by the ANR project DESIRE (DESIgns for spatial Random fiElds), nb. 2011-IS01-001-01, joint with the Statistics Dept. of the JKU Linz (Austria). B. Gauthier has also been supported by the MRI Dept. of EdF Chatou from Sept. to Dec. 2014.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.ESAT-STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, KU LeuvenLeuvenBelgium
  2. 2.CNRS, Laboratoire I3S – UMR 7271 Université de Nice-Sophia Antipolis/CNRSNiceFrance

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