Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

  • David Ginsbourger
  • Nicolas Durrande
  • Olivier Roustant
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • David Ginsbourger
    • 1
  • Nicolas Durrande
    • 2
  • Olivier Roustant
    • 3
  1. 1.Institute of Mathematical Statistics and Actuarial ScienceUniversity of BernBernSwitzerland
  2. 2.Department of Computer ScienceThe University of SheffieldSheffieldUK
  3. 3.FAYOL-EMSE, LSTIEcole Nationale Supérieure des Mines de Saint-EtienneSaint-EtienneFrance

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