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ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

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  • Durrande, N.
  • Ginsbourger, D.
  • Roustant, O.
  • Carraro, L.

Abstract

Given a reproducing kernel Hilbert space (H,〈.,.〉) of real-valued functions and a suitable measure μ over the source space D⊂R, we decompose H as the sum of a subspace of centered functions for μ and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

Suggested Citation

  • Durrande, N. & Ginsbourger, D. & Roustant, O. & Carraro, L., 2013. "ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 57-67.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:57-67
    DOI: 10.1016/j.jmva.2012.08.016
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    References listed on IDEAS

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    1. Marrel, Amandine & Iooss, Bertrand & Laurent, Béatrice & Roustant, Olivier, 2009. "Calculations of Sobol indices for the Gaussian process metamodel," Reliability Engineering and System Safety, Elsevier, vol. 94(3), pages 742-751.
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    1. Emanuele Borgonovo & Elmar Plischke & Giovanni Rabitti, 2022. "Interactions and computer experiments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1274-1303, September.
    2. Pronzato, Luc, 2019. "Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol’ indices and experimental design," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 93-109.
    3. Xuefei Lu & Alessandro Rudi & Emanuele Borgonovo & Lorenzo Rosasco, 2020. "Faster Kriging: Facing High-Dimensional Simulators," Operations Research, INFORMS, vol. 68(1), pages 233-249, January.
    4. Heredia, María Belén & Prieur, Clémentine & Eckert, Nicolas, 2021. "Nonparametric estimation of aggregated Sobol’ indices: Application to a depth averaged snow avalanche model," Reliability Engineering and System Safety, Elsevier, vol. 212(C).

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