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Support indices: Measuring the effect of input variables over their supports

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  • Fruth, J.
  • Roustant, O.
  • Kuhnt, S.

Abstract

Two new sensitivity indices are presented which give an original solution to the question in sensitivity analysis of how to determine regions within the input space for which the model variation is high. The indices, as functions over the input domain, give insight into the local influence of input variables over the whole domain when the other variables lie in the global domain. They can serve as an informative extension to a standard analysis and in addition are especially helpful in the specification of the input domain, a critical, but often vaguely handled issue in sensitivity analysis. In the usual framework of independent continuous input variables, we present theoretical results that show an asymptotic connection between the presented indices and Sobol’ indices, valid for general probability distribution functions. Finally, we show how the indices can be successfully applied on analytical examples and on a real application.

Suggested Citation

  • Fruth, J. & Roustant, O. & Kuhnt, S., 2019. "Support indices: Measuring the effect of input variables over their supports," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 17-27.
    • Handle: RePEc:eee:reensy:v:187:y:2019:i:c:p:17-27
    DOI: 10.1016/j.ress.2018.07.026
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    References listed on IDEAS

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    1. Kucherenko, S. & Rodriguez-Fernandez, M. & Pantelides, C. & Shah, N., 2009. "Monte Carlo evaluation of derivative-based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1135-1148.
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    4. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).
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    6. Lamboni, M. & Iooss, B. & Popelin, A.-L. & Gamboa, F., 2013. "Derivative-based global sensitivity measures: General links with Sobol’ indices and numerical tests," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 45-54.
    7. Sobol’, I.M. & Kucherenko, S., 2009. "Derivative based global sensitivity measures and their link with global sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3009-3017.
    8. Li, Luyi & Lu, Zhenzhou & Hu, JiXiang, 2014. "A new kind of regional importance measure of the input variable and its state dependent parameter solution," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 1-16.
    9. Wei, Pengfei & Lu, Zhenzhou & Ruan, Wenbin & Song, Jingwen, 2014. "Regional sensitivity analysis using revised mean and variance ratio functions," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 121-135.
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    Cited by:

    1. Nogal, M. & Nogal, A., 2021. "Sensitivity method for extreme-based engineering problems," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

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