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Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models

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  • Lamboni, Matieyendou
  • Monod, Hervé
  • Makowski, David

Abstract

Many dynamic models are used for risk assessment and decision support in ecology and crop science. Such models generate time-dependent model predictions, with time either discretised or continuous. Their global sensitivity analysis is usually applied separately on each time output, but Campbell et al. (2006 [1]) advocated global sensitivity analyses on the expansion of the dynamics in a well-chosen functional basis. This paper focuses on the particular case when principal components analysis is combined with analysis of variance. In addition to the indices associated with the principal components, generalised sensitivity indices are proposed to synthesize the influence of each parameter on the whole time series output. Index definitions are given when the uncertainty on the input factors is either discrete or continuous and when the dynamic model is either discrete or functional. A general estimation algorithm is proposed, based on classical methods of global sensitivity analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:4:p:450-459
    DOI: 10.1016/j.ress.2010.12.002
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    References listed on IDEAS

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    1. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    2. Campbell, Katherine & McKay, Michael D. & Williams, Brian J., 2006. "Sensitivity analysis when model outputs are functions," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1468-1472.
    3. Besse, Philippe, 1992. "PCA stability and choice of dimensionality," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 405-410, April.
    4. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    5. Makowski, David & Naud, Cédric & Jeuffroy, Marie-Hélène & Barbottin, Aude & Monod, Hervé, 2006. "Global sensitivity analysis for calculating the contribution of genetic parameters to the variance of crop model prediction," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1142-1147.
    6. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
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