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The identification of model effective dimensions using global sensitivity analysis

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  • Kucherenko, Sergei
  • Feil, Balazs
  • Shah, Nilay
  • Mauntz, Wolfgang

Abstract

It is shown that the effective dimensions can be estimated at reasonable computational costs using variance based global sensitivity analysis. Namely, the effective dimension in the truncation sense can be found by using the Sobol' sensitivity indices for subsets of variables. The effective dimension in the superposition sense can be estimated by using the first order effects and the total Sobol' sensitivity indices. The classification of some important classes of integrable functions based on their effective dimension is proposed. It is shown that it can be used for the prediction of the QMC efficiency. Results of numerical tests verify the prediction of the developed techniques.

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  • Kucherenko, Sergei & Feil, Balazs & Shah, Nilay & Mauntz, Wolfgang, 2011. "The identification of model effective dimensions using global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 440-449.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:4:p:440-449
    DOI: 10.1016/j.ress.2010.11.003
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    References listed on IDEAS

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    Cited by:

    1. Kucherenko, Sergei & Song, Shufang & Wang, Lu, 2019. "Quantile based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 35-48.
    2. Lambert, Romain S.C. & Lemke, Frank & Kucherenko, Sergei S. & Song, Shufang & Shah, Nilay, 2016. "Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 42-54.
    3. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Regional and parametric sensitivity analysis of Sobol׳ indices," Reliability Engineering and System Safety, Elsevier, vol. 137(C), pages 87-100.
    4. Becker, William, 2020. "Metafunctions for benchmarking in sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    5. 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.
    6. Spiessl, Sabine M. & Kucherenko, Sergei & Becker, Dirk-A. & Zaccheus, Oluyemi, 2019. "Higher-order sensitivity analysis of a final repository model with discontinuous behaviour using the RS-HDMR meta-modeling approach," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 149-158.
    7. Kucherenko, S. & Delpuech, B. & Iooss, B. & Tarantola, S., 2015. "Application of the control variate technique to estimation of total sensitivity indices," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 251-259.
    8. 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.
    9. Kucherenko, S. & Song, S., 2017. "Different numerical estimators for main effect global sensitivity indices," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 222-238.
    10. Sun, Xifu & Croke, Barry & Roberts, Stephen & Jakeman, Anthony, 2021. "Comparing methods of randomizing Sobol′ sequences for improving uncertainty of metrics in variance-based global sensitivity estimation," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    11. 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.
    12. Lo Piano, Samuele & Ferretti, Federico & Puy, Arnald & Albrecht, Daniel & Saltelli, Andrea, 2021. "Variance-based sensitivity analysis: The quest for better estimators and designs between explorativity and economy," Reliability Engineering and System Safety, Elsevier, vol. 206(C).
    13. Francesca Di Girolamo & Henrik Jonsson & Francesca Campolongo & Wim Schoutens, 2012. "Sense and Sensitivity: An Input Space Odyssey for Asset-Backed Security Ratings," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 3(4), pages 46-68, October.
    14. Xiao, Sinan & Lu, Zhenzhou & Wang, Pan, 2018. "Multivariate global sensitivity analysis for dynamic models based on wavelet analysis," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 20-30.
    15. 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.
    16. Wu, Zeping & Wang, Wenjie & Wang, Donghui & Zhao, Kun & Zhang, Weihua, 2019. "Global sensitivity analysis using orthogonal augmented radial basis function," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 291-302.
    17. 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.
    18. Anstett-Collin, F. & Goffart, J. & Mara, T. & Denis-Vidal, L., 2015. "Sensitivity analysis of complex models: Coping with dynamic and static inputs," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 268-275.
    19. Kucherenko, S. & Klymenko, O.V. & Shah, N., 2017. "Sobol' indices for problems defined in non-rectangular domains," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 218-231.
    20. Bouchkira, Ilias & Latifi, Abderrazak M. & Khamar, Lhachmi & Benjelloun, Saad, 2021. "Global sensitivity based estimability analysis for the parameter identification of Pitzer’s thermodynamic model," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    21. Ge, Qiao & Ciuffo, Biagio & Menendez, Monica, 2015. "Combining screening and metamodel-based methods: An efficient sequential approach for the sensitivity analysis of model outputs," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 334-344.
    22. Horiguchi, Akira & Pratola, Matthew T. & Santner, Thomas J., 2021. "Assessing variable activity for Bayesian regression trees," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    23. 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.
    24. Liu, Fuchao & Wei, Pengfei & Tang, Chenghu & Wang, Pan & Yue, Zhufeng, 2019. "Global sensitivity analysis for multivariate outputs based on multiple response Gaussian process model," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 287-298.
    25. Marco Bianchetti & Sergei Kucherenko & Stefano Scoleri, 2015. "Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis," Papers 1504.02896, arXiv.org.

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