IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v86y2024i2d10.1007_s13171-024-00354-w.html
   My bibliography  Save this article

Kernel-based Measures of Association Between Inputs and Outputs Using ANOVA

Author

Listed:
  • Matieyendou Lamboni

    (University of Guyane
    University of Guyane, University of Réunion, IRD, University of Montpellier)

Abstract

ANOVA decomposition of a function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate reproducing kernel Hilbert space regarding their distributions, we propose an efficient statistical test of independence between the input variables and output variable(s). The resulting test statistic leads to new dependence measures of association between inputs and outputs that allow for i) dealing with any distribution of AFs, including the Cauchy distribution, ii) accounting for the necessary or desirable moments of AFs and the interactions among the input variables. In uncertainty quantification for mathematical models, a number of existing measures are special cases of this framework. We then provide unified and general global sensitivity indices and their consistent estimators, including asymptotic distributions. For Gaussian-distributed AFs, we obtain Sobol’ indices and dependent generalized sensitivity indices using quadratic kernels.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:2:d:10.1007_s13171-024-00354-w
    DOI: 10.1007/s13171-024-00354-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-024-00354-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-024-00354-w?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. 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.
    2. 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.
    3. 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.
    4. Lamboni, Matieyendou, 2020. "Derivative-based generalized sensitivity indices and Sobol’ indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 236-256.
    5. 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.
    6. 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.
    7. Jeremy E. Oakley & Anthony O'Hagan, 2004. "Probabilistic sensitivity analysis of complex models: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 751-769, August.
    8. Elmar Plischke & Emanuele Borgonovo, 2020. "Fighting the Curse of Sparsity: Probabilistic Sensitivity Measures From Cumulative Distribution Functions," Risk Analysis, John Wiley & Sons, vol. 40(12), pages 2639-2660, December.
    9. Kojadinovic, Ivan & Holmes, Mark, 2009. "Tests of independence among continuous random vectors based on Cramr-von Mises functionals of the empirical copula process," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1137-1154, July.
    10. Lamboni, Matieyendou, 2022. "Efficient dependency models: Simulating dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 199-217.
    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.
    Full references (including those not matched with items on IDEAS)

    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 & Kucherenko, Sergei, 2021. "Multivariate sensitivity analysis and derivative-based global sensitivity measures with dependent variables," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    2. 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.
    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.
    4. 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.
    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.
    6. 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.
    7. 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.
    8. Matieyendou Lamboni, 2024. "Optimal Estimators of Cross-Partial Derivatives and Surrogates of Functions," Stats, MDPI, vol. 7(3), pages 1-22, July.
    9. Lamboni, Matieyendou, 2022. "Efficient dependency models: Simulating dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 199-217.
    10. 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.
    11. 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.
    12. Chen, Xin & Molina-Cristóbal, Arturo & Guenov, Marin D. & Riaz, Atif, 2019. "Efficient method for variance-based sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 97-115.
    13. Lamboni, Matieyendou, 2020. "Derivative-based generalized sensitivity indices and Sobol’ indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 236-256.
    14. Zhang, Kaichao & Lu, Zhenzhou & Cheng, Kai & Wang, Laijun & Guo, Yanling, 2020. "Global sensitivity analysis for multivariate output model and dynamic models," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    15. Li, Min & Wang, Ruo-Qian & Jia, Gaofeng, 2020. "Efficient dimension reduction and surrogate-based sensitivity analysis for expensive models with high-dimensional outputs," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    16. Nagel, Joseph B. & Rieckermann, Jörg & Sudret, Bruno, 2020. "Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: Application to urban drainage simulation," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    17. Priscilla Avegliano & Jaime Simão Sichman, 2023. "Equation-Based Versus Agent-Based Models: Why Not Embrace Both for an Efficient Parameter Calibration?," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 26(4), pages 1-3.
    18. 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.
    19. Daniel W. Gladish & Ross Darnell & Peter J. Thorburn & Bhakti Haldankar, 2019. "Emulated Multivariate Global Sensitivity Analysis for Complex Computer Models Applied to Agricultural Simulators," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 130-153, March.
    20. 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.

    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:spr:sankha:v:86:y:2024:i:2:d:10.1007_s13171-024-00354-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.