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Distributions of Outputs Given Subsets of Inputs and Dependent Generalized Sensitivity Indices

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  • Matieyendou Lamboni

    (Department DFR-ST, University of Guyane, 97346 Cayenne, France
    228-UMR Espace-Dev, University of Guyane, University of Réunion, IRD, University of Montpellier, 34090 Montpellier, France)

Abstract

Better understanding mathematical and numerical models often requires investigating the impacts of inputs on the model outputs, as well as interactions. Quantifying such effects for models with non-independent input variables (NIVs) relies on conditional distributions of the outputs given every subset of inputs. In this paper, by firstly providing additional dependency models of NIVs, functional outputs are composed by dependency models (yielding equivalent representations of outputs) to derive distributions of outputs conditional on inputs. We then provide an algorithm for selecting the necessary and sufficient equivalent representations that allow for obtaining all the conditional distributions of outputs given every subset of inputs, and for assessing the main, total, and interaction effects (i.e., indices) of every subset of NIVs. Unbiased estimators of covariances of sensitivity functionals and consistent estimators of such indices are derived by distinguishing the case of the multivariate and/or functional outputs, including dynamic models. Finally, analytical results and numerical results are provided, including an illustration based on a dynamic model.

Suggested Citation

  • Matieyendou Lamboni, 2025. "Distributions of Outputs Given Subsets of Inputs and Dependent Generalized Sensitivity Indices," Mathematics, MDPI, vol. 13(5), pages 1-22, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:766-:d:1600239
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    References listed on IDEAS

    as
    1. Matieyendou Lamboni, 2023. "On Exact Distribution for Multivariate Weighted Distributions and Classification," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    2. Hao, Wenrui & Lu, Zhenzhou & Wei, Pengfei, 2013. "Uncertainty importance measure for models with correlated normal variables," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 48-58.
    3. 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).
    4. Matieyendou Lamboni, 2024. "Kernel-based Measures of Association Between Inputs and Outputs Using ANOVA," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 790-826, August.
    5. Lamboni, Matieyendou, 2020. "Derivative-based generalized sensitivity indices and Sobol’ indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 236-256.
    6. Xiao, Sinan & Lu, Zhenzhou & Xu, Liyang, 2017. "Multivariate sensitivity analysis based on the direction of eigen space through principal component analysis," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 1-10.
    7. Mara, Thierry A. & Tarantola, Stefano, 2012. "Variance-based sensitivity indices for models with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 115-121.
    8. Lamboni, Matieyendou & Monod, Hervé & Makowski, David, 2011. "Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 450-459.
    9. Lamboni, Matieyendou, 2019. "Multivariate sensitivity analysis: Minimum variance unbiased estimators of the first-order and total-effect covariance matrices," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 67-92.
    10. Smith, Michael & Min, Aleksey & Almeida, Carlos & Czado, Claudia, 2010. "Modeling Longitudinal Data Using a Pair-Copula Decomposition of Serial Dependence," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1467-1479.
    11. 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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