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Sensitivity indices for independent groups of variables

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  • Broto, Baptiste
  • Bachoc, François
  • Depecker, Marine
  • Martinez, Jean-Marc

Abstract

In this paper, we study sensitivity indices for independent groups of variables and we look at the particular case of block-additive models. We show in this case that most of the Sobol indices are equal to zero and that Shapley effects can be estimated more efficiently. We then apply this study to Gaussian linear models, and we provide an efficient algorithm to compute the theoretical sensitivity indices. In numerical experiments, we show that this algorithm compares favourably to other existing methods. We also use the theoretical results to improve the estimation of the Shapley effects for general models, when the inputs form independent groups of variables.

Suggested Citation

  • Broto, Baptiste & Bachoc, François & Depecker, Marine & Martinez, Jean-Marc, 2019. "Sensitivity indices for independent groups of variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 19-31.
    • Handle: RePEc:eee:matcom:v:163:y:2019:i:c:p:19-31
    DOI: 10.1016/j.matcom.2019.02.008
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    References listed on IDEAS

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    1. Emanuele Borgonovo & Gordon B. Hazen & Elmar Plischke, 2016. "A Common Rationale for Global Sensitivity Measures and Their Estimation," Risk Analysis, John Wiley & Sons, vol. 36(10), pages 1871-1895, October.
    2. 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.
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    4. Borgonovo, E., 2007. "A new uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 771-784.
    5. Jacques, Julien & Lavergne, Christian & Devictor, Nicolas, 2006. "Sensitivity analysis in presence of model uncertainty and correlated inputs," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1126-1134.
    6. Hammer, Hugo & Tjelmeland, Håkon, 2011. "Approximate forward-backward algorithm for a switching linear Gaussian model," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 154-167, January.
    7. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
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    Cited by:

    1. Vuillod, Bruno & Montemurro, Marco & Panettieri, Enrico & Hallo, Ludovic, 2023. "A comparison between Sobol’s indices and Shapley’s effect for global sensitivity analysis of systems with independent input variables," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    2. Eranga M. Wimalasiri & Ebrahim Jahanshiri & Tengku Adhwa Syaherah Tengku Mohd Suhairi & Hasika Udayangani & Ranjith B. Mapa & Asha S. Karunaratne & Lal P. Vidhanarachchi & Sayed N. Azam-Ali, 2020. "Basic Soil Data Requirements for Process-Based Crop Models as a Basis for Crop Diversification," Sustainability, MDPI, vol. 12(18), pages 1-20, September.

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