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Derivative-based generalized sensitivity indices and Sobol’ indices

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  • Lamboni, Matieyendou

Abstract

In uncertainty quantification, multivariate sensitivity analysis (MSA), including variance-based sensitivity analysis, and derivative global sensitivity measure (DGSM) are widely used for assessing the effects of input factors on the model outputs. While MSA allows for identifying the order and the strength of interactions among inputs, DGSM provides only a global effect of inputs by making use of model derivatives. It is interesting to combine the advantages of both approaches and to come up with generalized sensitivity indices (GSIs) from MSA based on model derivatives. First, we derive the mathematical expressions of the total effect and total-interaction effect functionals based on derivatives. Second, we construct minimum variance unbiased estimators (MVUEs) of the total-effect and total-interaction effect covariance matrices, and third, we provide the estimators of the total and total-interaction GSIs as well as their consistency and asymptotic normality. Finally, we demonstrate the applicability of these new results by means of simulations.

Suggested Citation

  • Lamboni, Matieyendou, 2020. "Derivative-based generalized sensitivity indices and Sobol’ indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 236-256.
    • Handle: RePEc:eee:matcom:v:170:y:2020:i:c:p:236-256
    DOI: 10.1016/j.matcom.2019.10.017
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    References listed on IDEAS

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    Cited by:

    1. Matieyendou Lamboni, 2024. "Optimal Estimators of Cross-Partial Derivatives and Surrogates of Functions," Stats, MDPI, vol. 7(3), pages 1-22, July.
    2. 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).
    3. 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.
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    5. 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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