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Estimation of global sensitivity indices for models with dependent variables. (English) Zbl 1261.62062

Summary: A novel approach for estimation of variance-based sensitivity indices for models with dependent variables is presented. Both the first order and total sensitivity indices are derived as generalizations of Sobol’ sensitivity indices. Formulas and Monte Carlo numerical estimates similar to Sobol’ formulas are derived. A copula-based approach is proposed for sampling from arbitrary multivariate probability distributions. A good agreement between analytical and numerical values of the first order and total indices for considered test cases is obtained. The behavior of sensitivity indices depends on the relative predominance of interactions and correlations. The method is shown to be efficient and general.

MSC:

62H99 Multivariate analysis
62H20 Measures of association (correlation, canonical correlation, etc.)
65C05 Monte Carlo methods

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References:

[1] Saltelli, A.; Ratto, M.; Tarantola, S.; Campolongo, F., Chem. Rev., 105, 2811 (2005)
[2] Sobolʼ, I.; Kucherenko, S., Wilmott, 56 (2005)
[3] Saltelli, A.; Annoni, P.; Azzini, I.; Campolongo, F.; Ratto, M.; Tarantola, S., Comput. Phys. Commun., 181, 259 (2010)
[4] Sobolʼ, I., Mat. Model.. Mat. Model., Mat. Model. Comp. Exper., 26, 407 (1993), (in Russian); translated in: I.M. Sobolʼ
[5] Jacques, J.; Lavergne, C.; Devictor, N., Rel. Eng. Syst. Safety, 91, 1126 (2006)
[6] Keitel, H.; Dimmig-Osburg, A., Eng. Struct., 32, 3758 (2010)
[7] Ades, A. E.; Claxton, K.; Sculpher, M., Health Econ., 15, 373 (2006)
[8] Ferson, S.; Burgman, M., Biol. Conserv., 73, 101 (1995)
[9] Brell, G.; Li, G.; Rabitz, H., J. Chem. Phys., 132, 174103 (2010)
[10] T. Bedford, in: Proceedings of the Second International Symposium on Sensitivity Analysis of Model Output, Venice, 1998.; T. Bedford, in: Proceedings of the Second International Symposium on Sensitivity Analysis of Model Output, Venice, 1998.
[11] Saltelli, A.; Tarantola, S., J. Amer. Statist. Assoc., 97, 702 (2002)
[12] Xu, C.; Gertner, G. Z., Rel. Eng. Syst. Safety, 93, 1563 (2008)
[13] Li, G.; Rabitz, H.; Yelvington, P.; Oluwole, O.; Bacon, F.; Kolb, C.; Schoendorf, J., J. Phys. Chem. A, 114, 6022 (2010)
[14] Sobolʼ, I., Math. Comput. Simulation, 55, 271 (2001)
[15] Sobolʼ, I.; Tarantola, S.; Gatelli, D.; Kucherenko, S.; Mauntz, W., Rel. Eng. Syst. Safety, 92, 957 (2007)
[16] Kucherenko, S.; Feil, B.; Shah, N.; Mauntz, W., Rel. Eng. Syst. Safety, 96, 440 (2011)
[17] Saltelli, A., Comput. Phys. Commun., 145, 280 (2002)
[18] Jansen, M. J.W.; Rossing, W. A.H.; Daamen, R. A., (Grasman, J.; Van Straten, G., Predictability and Nonlinear Modelling in Natural Sciences and Economics (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), 334
[19] Cherubini, U.; Luciano, E.; Vecchiato, W., Copula Methods in Finance (2004), Wiley · Zbl 1163.62081
[20] McNeil, A. J.; Frey, R.; Embrechts, P., Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton Series in Finance (2005) · Zbl 1089.91037
[21] Sklar, A., Publ. Inst. Statist. Univ. Paris, 8, 229 (1959)
[22] Liu, P. L.; Der Kiureghian, A., Probab. Eng. Mech., 1, 105 (1986)
[23] Sobol, I.; Myshetskaya, E., Monte Carlo Methods Appl., 1, 67 (2003)
[24] Bratley, P.; Fox, B., ACM Trans. Math. Software, 14, 88 (1988)
[25] Niederreiter, H., Random Number Generation and Quasi-Monte Carlo Methods (1992), SIAM · Zbl 0761.65002
[26] Sobolʼ, I., Math. Comput. Simulation, 47, 103 (1998)
[27] Da Veiga, S.; Whal, F.; Gamboa, F., Technometrics, 51, 452 (2009)
[28] Saltelli, A.; Ratto, M.; Tarantola, S.; Campolongo, F., Global Sensitivity Analysis (2004), Wiley
[29] T. Ishigami, T. Homma, in: Proceedings of ISUMA, First International Symposium on Uncertainty Modelling and Analysis, 1990, p. 398.; T. Ishigami, T. Homma, in: Proceedings of ISUMA, First International Symposium on Uncertainty Modelling and Analysis, 1990, p. 398.
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