IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v187y2019icp17-27.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832017307111
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2018.07.026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Lu, Zhan-Qian, 1996. "Multivariate Locally Weighted Polynomial Fitting and Partial Derivative Estimation," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 187-205, November.
    3. 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.
    4. 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.
    5. 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.
    6. Pannier, S. & Graf, W., 2015. "Sectional global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 110-117.
    7. 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).
    8. Roustant, O. & Fruth, J. & Iooss, B. & Kuhnt, S., 2014. "Crossed-derivative based sensitivity measures for interaction screening," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 105-118.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lamboni, Matieyendou, 2021. "Derivative-based integral equalities and inequality: A proxy-measure for sensitivity analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 137-161.
    2. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    3. Lamboni, Matieyendou, 2020. "Derivative-based generalized sensitivity indices and Sobol’ indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 236-256.
    4. Matieyendou Lamboni, 2020. "Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices," Statistical Papers, Springer, vol. 61(5), pages 1939-1970, October.
    5. Ge, Qiao & Menendez, Monica, 2017. "Extending Morris method for qualitative global sensitivity analysis of models with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 162(C), pages 28-39.
    6. Matieyendou Lamboni, 2018. "Global sensitivity analysis: a generalized, unbiased and optimal estimator of total-effect variance," Statistical Papers, Springer, vol. 59(1), pages 361-386, March.
    7. Lamboni, Matieyendou, 2022. "Weak derivative-based expansion of functions: ANOVA and some inequalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 691-718.
    8. Zhou, Changcong & Shi, Zhuangke & Kucherenko, Sergei & Zhao, Haodong, 2022. "A unified approach for global sensitivity analysis based on active subspace and Kriging," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    9. Nogal, M. & Nogal, A., 2021. "Sensitivity method for extreme-based engineering problems," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    10. Sinan Xiao & Zhenzhou Lu & Pan Wang, 2018. "Multivariate Global Sensitivity Analysis Based on Distance Components Decomposition," Risk Analysis, John Wiley & Sons, vol. 38(12), pages 2703-2721, December.
    11. Pannier, S. & Graf, W., 2015. "Sectional global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 110-117.
    12. Roustant, O. & Fruth, J. & Iooss, B. & Kuhnt, S., 2014. "Crossed-derivative based sensitivity measures for interaction screening," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 105-118.
    13. Lamboni, Matieyendou & Kucherenko, Sergei, 2021. "Multivariate sensitivity analysis and derivative-based global sensitivity measures with dependent variables," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    14. Isadora Antoniano‐Villalobos & Emanuele Borgonovo & Sumeda Siriwardena, 2018. "Which Parameters Are Important? Differential Importance Under Uncertainty," Risk Analysis, John Wiley & Sons, vol. 38(11), pages 2459-2477, November.
    15. Cheng, Lei & Lu, Zhenzhou & Zhang, Leigang, 2015. "Application of Rejection Sampling based methodology to variance based parametric sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 9-18.
    16. Song, Shufang & Zhou, Tong & Wang, Lu & Kucherenko, Sergei & Lu, Zhenzhou, 2019. "Derivative-based new upper bound of Sobol’ sensitivity measure," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 142-148.
    17. Kucherenko, Sergei & Song, Shufang & Wang, Lu, 2019. "Quantile based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 35-48.
    18. Wu, Zeping & Wang, Donghui & Okolo N, Patrick & Hu, Fan & Zhang, Weihua, 2016. "Global sensitivity analysis using a Gaussian Radial Basis Function metamodel," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 171-179.
    19. Liu, Yaning & Yousuff Hussaini, M. & Ökten, Giray, 2016. "Accurate construction of high dimensional model representation with applications to uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 281-295.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:187:y:2019:i:c:p:17-27. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.