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Derivative based global sensitivity measures and their link with global sensitivity indices

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  • Sobol’, I.M.
  • Kucherenko, S.

Abstract

A model function f(x1,…,xn) defined in the unit hypercube Hn with Lebesque measure dx=dx1…dxn is considered. If the function is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors xi or groups of such factors. Alternative estimators that require less computer time can also be used. If the function f is differentiable, functionals depending on ∂f/∂xi have been suggested as estimators for the influence of xi. The Morris importance measure modified by Campolongo, Cariboni and Saltelli μ* is an approximation of the functional μi=∫Hn∂f/∂xidx.

Suggested Citation

  • Sobol’, I.M. & Kucherenko, S., 2009. "Derivative based global sensitivity measures and their link with global sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3009-3017.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:10:p:3009-3017
    DOI: 10.1016/j.matcom.2009.01.023
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    References listed on IDEAS

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    1. 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.
    2. Sobol′ , I.M, 2001. "Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 271-280.
    3. Sobol’, I.M. & Tarantola, S. & Gatelli, D. & Kucherenko, S.S. & Mauntz, W., 2007. "Estimating the approximation error when fixing unessential factors in global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 92(7), pages 957-960.
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