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Variance-based sensitivity indices for models with dependent inputs

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  • Mara, Thierry A.
  • Tarantola, Stefano

Abstract

Computational models are intensively used in engineering for risk analysis or prediction of future outcomes. Uncertainty and sensitivity analyses are of great help in these purposes. Although several methods exist to perform variance-based sensitivity analysis of model output with independent inputs only a few are proposed in the literature in the case of dependent inputs. This is explained by the fact that the theoretical framework for the independent case is set and a univocal set of variance-based sensitivity indices is defined. In the present work, we propose a set of variance-based sensitivity indices to perform sensitivity analysis of models with dependent inputs. These measures allow us to distinguish between the mutual dependent contribution and the independent contribution of an input to the model response variance. Their definition relies on a specific orthogonalisation of the inputs and ANOVA-representations of the model output. In the applications, we show the interest of the new sensitivity indices for model simplification setting.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:107:y:2012:i:c:p:115-121
    DOI: 10.1016/j.ress.2011.08.008
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    References listed on IDEAS

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    1. Saltelli, Andrea & Ratto, Marco & Tarantola, Stefano & Campolongo, Francesca, 2006. "Sensitivity analysis practices: Strategies for model-based inference," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1109-1125.
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    6. Saltelli A. & Tarantola S., 2002. "On the Relative Importance of Input Factors in Mathematical Models: Safety Assessment for Nuclear Waste Disposal," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 702-709, September.
    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. Mara, Thierry Alex, 2009. "Extension of the RBD-FAST method to the computation of global sensitivity indices," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1274-1281.
    9. 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.
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