Abstract
The variance-based method of Sobol’ sensitivity indices is very popular among practitioners due to its efficiency and easiness of interpretation. However, for high-dimensional models the direct application of this method can be very time-consuming and prohibitively expensive to use. One of the alternative global sensitivity analysis methods known as the method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a link with the Morris screening method and Sobol’ sensitivity indices. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that for estimation of Sobol’ sensitivity indices. We present a survey of recent advances in DGSM and new results concerning new lower and upper bounds on the values of Sobol’ total sensitivity indices \(S_i^{tot} \). Using these bounds it is possible in most cases to get a good practical estimation of the values of \(S_i^{tot} \). Several examples are used to illustrate an application of DGSM.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Griewank, A., Walther, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM Philadelphia, Philadelphia (2008)
Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities, 2nd edn. Cambridge University Press, Cambridge (1973)
Homma, T., Saltelli, A.: Importance measures in global sensitivity analysis of model output. Reliab. Eng. Syst. Saf. 52(1), 1–17 (1996)
Jansen, K., Leovey, H., Nube, A., Griewank, A., Mueller-Preussker, M.: A first look at quasi-Monte Carlo for lattice field theory problems. Comput. Phys. Commun. 185, 948–959 (2014)
Kiparissides, A., Kucherenko, S., Mantalaris, A., Pistikopoulos, E.N.: Global sensitivity analysis challenges in biological systems modeling. J. Ind. Eng. Chem. Res. 48(15), 7168–7180 (2009)
Kucherenko, S., Rodriguez-Fernandez, M., Pantelides, C., Shah, N.: Monte Carlo evaluation of derivative based global sensitivity measures. Reliab. Eng. Syst. Saf. 94(7), 1135–1148 (2009)
Lamboni, M., Iooss, B., Popelin, A.L., Gamboa, F.: Derivative based global sensitivity measures: general links with Sobol’s indices and numerical tests. Math. Comput. Simul. 87, 45–54 (2013)
Morris, M.D.: Factorial sampling plans for preliminary computational experiments. Technometrics 33, 161–174 (1991)
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.: Global Sensitivity Analysis: The Primer. Wiley, New York (2008)
Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., Tarantola, S.: Variance based sensitivity analysis of model output: design and estimator for the total sensitivity index. Comput. Phys. Commun. 181(2), 259–270 (2010)
I.M. Sobol’ Sensitivity estimates for nonlinear mathematical models. Matem. Modelirovanie , 2: 112-118, 1990 (in Russian). English translation: Math. Modelling and Comput. Experiment, 1(4):407–414, 1993
Sobol’, I.M., Gershman, A.: On an altenative global sensitivity estimators. Proc SAMO, Belgirate 1995, 40–42 (1995)
Sobol’, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55(1–3), 271–280 (2001)
Sobol’, I.M., Kucherenko, S.: Global sensitivity indices for nonlinear mathematical models. Rev. Wilmott Mag. 1, 56–61 (2005)
Sobol’, I.M., Kucherenko, S.: Derivative based global sensitivity measures and their link with global sensitivity indices. Math. Comput. Simul. 79(10), 3009–3017 (2009)
Sobol’, I.M., Kucherenko, S.: A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices. Comput. Phys. Commun. 181(7), 1212–1217 (2010)
Acknowledgments
The authors would like to thank Prof. I. Sobol’ his invaluable contributions to this work. Authors also gratefully acknowledge the financial support by the EPSRC grant EP/H03126X/1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Kucherenko, S., Song, S. (2016). Derivative-Based Global Sensitivity Measures and Their Link with Sobol’ Sensitivity Indices. In: Cools, R., Nuyens, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-319-33507-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-33507-0_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33505-6
Online ISBN: 978-3-319-33507-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)