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Relationship between sensitivity indices defined by variance- and covariance-based methods

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  • Li, Genyuan
  • Rabitz, Herschel

Abstract

Sensitivity analysis is a challenge to perform with correlated variables, as often occur in practice. The variance-based methods for correlated variables use the same sensitivity indices defined for independent variables. The associate algorithms to determine the sensitivity indices are computationally demanding, and require explicit knowledge of the joint and conditional probability density function (pdf) of the input variables. As an alternative, a method referred to as structural and correlative sensitivity analysis (SCSA) based on a covariance decomposition has also been developed to fully quantify the deterministic and statistical contributions of independent and correlated variables, which can be applied in simulations as well as for laboratory/field data where the explicit forms of the function f(x) and the pdf are unknown. In this paper, we show that the sensitivity indices defined by the variance-based method may be re-expressed in terms of the SCSA sensitivity indices without further numerical computation, if the function f(x) and the pdf are known. If f(x) and the pdf are not known, the indices can still be accurately calculated from a single modest set of input-output data samples with SCSA.

Suggested Citation

  • Li, Genyuan & Rabitz, Herschel, 2017. "Relationship between sensitivity indices defined by variance- and covariance-based methods," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 136-157.
    • Handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:136-157
    DOI: 10.1016/j.ress.2017.05.038
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    References listed on IDEAS

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    Cited by:

    1. Xie, Xiangzhong & Schenkendorf, René & Krewer, Ulrike, 2019. "Efficient sensitivity analysis and interpretation of parameter correlations in chemical engineering," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 159-173.
    2. Mara, Thierry A. & Becker, William E., 2021. "Polynomial chaos expansion for sensitivity analysis of model output with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    3. Borgonovo, Emanuele & Buzzard, Gregery T. & Wendell, Richard E., 2018. "A global tolerance approach to sensitivity analysis in linear programming," European Journal of Operational Research, Elsevier, vol. 267(1), pages 321-337.

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