On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

Ginsbourger, David; Roustant, Olivier; Schuhmacher, Dominic; Durrande, Nicolas; Lenz, Nicolas (2016). On ANOVA Decompositions of Kernels and Gaussian Random Field Paths. In: Cools, Ronald; Nuyens, Dirk (eds.) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics: Vol. 163 (pp. 315-330). Cham: Springer International Publishing 10.1007/978-3-319-33507-0_15

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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
4d 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.

Item Type:

Book Section (Book Chapter)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Ginsbourger, David

Subjects:

500 Science > 510 Mathematics

ISSN:

2194-1009

ISBN:

978-3-319-33505-6

Series:

Springer Proceedings in Mathematics & Statistics

Publisher:

Springer International Publishing

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

20 Jul 2016 10:01

Last Modified:

20 Oct 2016 09:44

Publisher DOI:

10.1007/978-3-319-33507-0_15

URI:

https://boris.unibe.ch/id/eprint/83996

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