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Monte Carlo algorithms for evaluating Sobol’ sensitivity indices

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  • Dimov, I.
  • Georgieva, R.

Abstract

Sensitivity analysis is a powerful technique used to determine robustness, reliability and efficiency of a model. The main problem in this procedure is the evaluating total sensitivity indices that measure a parameter’s main effect and all the interactions involving that parameter. From a mathematical point of view this problem is presented by a set of multidimensional integrals. In this work a simple adaptive Monte Carlo technique for evaluating Sobol’ sensitivity indices is developed. A comparison of accuracy and complexity of plain Monte Carlo and adaptive Monte Carlo algorithms is presented. Numerical experiments for evaluating integrals of different dimensions are performed.

Suggested Citation

  • Dimov, I. & Georgieva, R., 2010. "Monte Carlo algorithms for evaluating Sobol’ sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 506-514.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:3:p:506-514
    DOI: 10.1016/j.matcom.2009.09.005
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    References listed on IDEAS

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    1. Karaivanova, Aneta & Dimov, Ivan, 1998. "Error analysis of an adaptive Monte Carlo method for numerical integration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 201-213.
    2. 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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    2. Nagel, Joseph B. & Rieckermann, Jörg & Sudret, Bruno, 2020. "Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: Application to urban drainage simulation," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    3. Verleysen, Kevin & Parente, Alessandro & Contino, Francesco, 2021. "How sensitive is a dynamic ammonia synthesis process? Global sensitivity analysis of a dynamic Haber-Bosch process (for flexible seasonal energy storage)," Energy, Elsevier, vol. 232(C).
    4. Xue-ping Chen & Jin-Guan Lin & Xiao-di Wang & Xing-fang Huang, 2015. "Further results on orthogonal arrays for the estimation of global sensitivity indices based on alias matrix," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 411-426, September.

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