Write an introduction to sensitivity analysis

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[jlakhlili]

References:

1. I. M. Sobol. Sensitivity estimates for nonlinear mathematical models. Mathematical Modelling and Computational Experiments, 1:407–414, 1993.
2. T. Homma and A. Saltelli. Importance measures in global sensitivity analysis of nonlinear models.
   Reliability Engineering & System Safety, 52(1):1–17, 1996.

[mbaudin47]

I suggest a few more recent references on the topic.

• M.J.W. Jansen, 1999, "Analysis of variance designs for model output", Computer Physics Communication, 117, 35–43
• "Making best use of model evaluations to compute sensitivity indices." Saltelli, A. Computer Physics Communication, 2002, 145, 580-297.
• "Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models", Andrea Saltelli Stefano Tarantola Francesca Campolongo Marco Ratto. John Wiley & Sons, Ltd (2004)
• Sobol, I.M., Tarantola, S., Gatelli, D., Kucherenko, S.S. and Mauntz, W. "Estimating the approximation errors when fixing unessential factors in global sensitivity analysis", Reliability Engineering and System Safety, 2007, 92, 957-960.
• I.M. Sobol, S. Tarantola, D. Gatelli, S.S. Kucherenko and W. Mauntz, 2007, "Estimating the approximation errors when
  fixing unessential factors in global sensitivity analysis", Reliability Engineering and System Safety, 92, 957–960.
• J-M. Martinez, 2011, "Analyse de sensibilite globale par decomposition de la variance", Presentation in the meeting of GdR
  Ondes and GdR MASCOT-NUM, January, 13th, 2011, Institut Henri Poincare, Paris, France
• Fabrice Gamboa, Alexandre Janon, Thierry Klein, Agnès Lagnoux. "Sensitivity analysis for multidimensional and functional
  outputs." 2013.
• Alexandre JANON, Thierry KLEIN, Agnès LAGNOUX, Maëlle NODET et Clémentine PRIEUR: "Asymptotic normality and efficiency of two Sobol index estimators." ESAIM : Probability and Statistics, 18:342–364, 2014. ISSN 1292-8100, 1262-3318
• "Sensitivity analysis", Emanuele Borgonovo, Springer (2017)
• Dumas A., "Lois asymptotiques des estimateurs des indices de Sobol’", Technical report, Phimeca, 2018.

The best estimator seems to be Janon (2014), but Martinez (2011) is much simpler. Dumas derived asymptotic estimators in 2018, based on an EDF contract.

A quick start for SA is provided here for OpenTURNS:

http://openturns.github.io/openturns/master/auto_reliability_sensitivity/sensitivity_analysis/plot_sensitivity_sobol.html

A recap of the basics is provided here:

http://openturns.github.io/openturns/master/theory/reliability_sensitivity/sensitivity_sobol.html

but a more detailed presentation is provided at:

https://github.com/mbaudin47/otsupgalilee-eleve/blob/master/4-Sensibilite/Sensibilite-Cours-nonlineaire.ipynb