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.)


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.


Finite Group Composition Operator Kriging Model Integrate Mean Square Error Additive Path 
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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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