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On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

  • David Ginsbourger
  • Olivier Roustant
  • Dominic Schuhmacher
  • Nicolas Durrande
  • Nicolas Lenz
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 163)

Abstract

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into \(4^{d}\) terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

Keywords

Gaussian processes Sensitivity analysis Kriging Covariance functions Conditional simulations 

Notes

Acknowledgments

The authors would like to thank Dario Azzimonti for proofreading, as well as the editors and an anonymous referee for their valuable comments and suggestions.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • David Ginsbourger
    • 1
    • 2
  • Olivier Roustant
    • 3
  • Dominic Schuhmacher
    • 4
  • Nicolas Durrande
    • 3
  • Nicolas Lenz
    • 5
  1. 1.Uncertainty Quantification and Optimal Design groupIdiap Research InstituteMartignySwitzerland
  2. 2.IMSV, Department of Mathematics and StatisticsUniversity of BernBernSwitzerland
  3. 3.Mines Saint-Etienne, UMR CNRS 6158, LIMOSSaint-etienneFrance
  4. 4.Institut für Mathematische StochastikGeorg-August-Universität GöttingenGöttingenGermany
  5. 5.geo7 AGBernSwitzerland

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