Kucherenko, S.; Tarantola, S.; Annoni, P. Estimation of global sensitivity indices for models with dependent variables. (English) Zbl 1261.62062 Comput. Phys. Commun. 183, No. 4, 937-946 (2012). 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. Cited in 1 ReviewCited in 26 Documents MSC: 62H99 Multivariate analysis 62H20 Measures of association (correlation, canonical correlation, etc.) 65C05 Monte Carlo methods Keywords:global sensitivity analysis; correlated inputs; Gaussian copula; quasi Monte Carlo methods; Sobol’ sensitivity indices; Sobol’ sequences Software:QRM PDFBibTeX XMLCite \textit{S. Kucherenko} et al., Comput. Phys. Commun. 183, No. 4, 937--946 (2012; Zbl 1261.62062) Full Text: DOI 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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.