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Crossed-derivative based sensitivity measures for interaction screening

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

Abstract

Global sensitivity analysis is used to quantify the influence of input variables on a numerical model output. Sobol’ indices are now classical sensitivity measures. However their estimation requires a large number of model evaluations, especially when interaction effects are of interest. Derivative-based global sensitivity measures (DGSM) have recently shown their efficiency for the identification of non-influential inputs. In this paper, we define crossed DGSM, based on second-order derivatives of model output. By using a L2-Poincaré inequality, we provide a crossed-DGSM based maximal bound for the superset importance (i.e. total Sobol’ indices of an interaction between two inputs). In order to apply this result, we discuss how to estimate the Poincaré constant for various probability distributions. Several analytical and numerical tests show the performance of the bound and allow to develop a generic strategy for interaction screening.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:105:y:2014:i:c:p:105-118
    DOI: 10.1016/j.matcom.2014.05.005
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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. 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.
    3. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
    4. 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.
    5. Storlie, Curtis B. & Helton, Jon C., 2008. "Multiple predictor smoothing methods for sensitivity analysis: Description of techniques," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 28-54.
    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.
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    Cited by:

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    3. 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.
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    5. 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.
    6. 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.
    7. 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.
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    9. 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.

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