In the past decade, Sobol’s variance decomposition has been used as a tool to assess how the output of a model is affected by the uncertainty on its input parameters. We show some links between global sensitivity analysis and stochastic ordering theory. More specifically, we study the influence of inputs’ distributions on Sobol indices in relation with stochastic orders. This gives an argument in favor of using Sobol’s indices in uncertainty quantification, as one indicator among others.
Accepté le :
DOI : 10.1051/ps/2018001
Mots-clés : Sensitivity analysis, Sobol indices, stochastic orders
@article{PS_2019__23__387_0,
author = {Cousin, A. and Janon, A. and Maume-Deschamps, V. and Niang, I.},
title = {On the consistency of {Sobol} indices with respect to stochastic ordering of model parameters},
journal = {ESAIM: Probability and Statistics},
pages = {387--408},
publisher = {EDP-Sciences},
volume = {23},
year = {2019},
doi = {10.1051/ps/2018001},
zbl = {1421.62053},
mrnumber = {3975701},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2018001/}
}
TY - JOUR AU - Cousin, A. AU - Janon, A. AU - Maume-Deschamps, V. AU - Niang, I. TI - On the consistency of Sobol indices with respect to stochastic ordering of model parameters JO - ESAIM: Probability and Statistics PY - 2019 SP - 387 EP - 408 VL - 23 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2018001/ DO - 10.1051/ps/2018001 LA - en ID - PS_2019__23__387_0 ER -
%0 Journal Article %A Cousin, A. %A Janon, A. %A Maume-Deschamps, V. %A Niang, I. %T On the consistency of Sobol indices with respect to stochastic ordering of model parameters %J ESAIM: Probability and Statistics %D 2019 %P 387-408 %V 23 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2018001/ %R 10.1051/ps/2018001 %G en %F PS_2019__23__387_0
Cousin, A.; Janon, A.; Maume-Deschamps, V.; Niang, I. On the consistency of Sobol indices with respect to stochastic ordering of model parameters. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 387-408. doi : 10.1051/ps/2018001. http://archive.numdam.org/articles/10.1051/ps/2018001/
[1] and , Monte Carlo estimation under different distributions using the same simulation. Technometrics 29 (1987) 153–160. | DOI | MR | Zbl
[2] , Measuring uncertainty importance: investigation and comparison of alternative approaches. Risk Anal. 26 (2006) 1349–1361. | DOI
[3] , A new uncertainty importance measure. Reliab. Eng. Syst. Saf. 92 (2007) 771–784. | DOI
[4] and , On the Quantification and Decomposition of Uncertainty, Vol. 41. Springer (2007). | MR
[5] and , Interest Rate Models – Theory and Practice. Springer (2006). | MR | Zbl
[6] and , Variance-based global sensitivity analysis via sparse-grid interpolation and cubature. Commun. Comput. Phys. 9 (2011) 542–567. | DOI | MR | Zbl
[7] and , Option valuation using the fast Fourier transform. J. Comput. Finance 2 (1999) 61–73. | DOI
[8] , , and , Actuarial Theory for Dependent Risks: Measures, Orders and Models. Wiley (2005). | DOI
[9] , and , A characterization of the dilation order and its applications. Stat. Pap. 40 (1999) 393–406. | DOI | MR | Zbl
[10] , A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6 (1993) 327–343. | DOI | MR | Zbl
[11] , and , Response surfaces and sensitivity analyses for an environmental model of dose calculations. Reliab. Eng. Syst. Saf. 91 (2006) 1241–1251. | DOI
[12] , Analyse de sensibilité et réduction de dimension. Application à l’océanographie. Ph.D. thesis, Université de Grenoble (2012).
[13] , and , The total time on test transform and the excess wealth stochastic orders of distributions. Adv. Appl. Probab. 34 (2002) 826–845. | DOI | MR | Zbl
[14] , , and , On decompositions of multivariate functions. Math. Comput. 79 (2010) 953–966. | DOI | MR | Zbl
[15] , , , , and , Density modification-based reliability sensitivity analysis. J. Stat. Comput. Simul. 85 (2015) 1200–1223. | DOI | MR | Zbl
[16] and , Variance-based sensitivity indices for models with dependent inputs. Reliab. Eng. Syst. Saf. 107 (2012) 115–121. | DOI
[17] and , Comparison Methods for Stochastic Models and Risks. Wiley (2002). | MR | Zbl
[18] , Sobol’indices and shapley value. SIAM/ASA J. Uncertain. Quantif. 2 (2014) 245–251. | DOI | MR | Zbl
[19] , , and , Multi-method global sensitivity analysis of flood inundation models. Adv. Water Resour. 31 (2008) 1–14. | DOI
[20] , and , Novel global sensitivity analysis methodology accounting for the crucial role of the distribution of input parameters: application to systems biology models. Int. J. Robust Nonlinear Control 22 (2012) 1082–1102. | DOI | MR | Zbl
[21] , , , , , , and , Global Sensitivity Analysis: The Primer. Wiley (2008). | MR | Zbl
[22] and , Two variability orders. Probab. Eng. Inf. Sci. 12 (1998) 1–23. | DOI | MR | Zbl
[23] and , Stochastic Orders. Springer (2007). | DOI | MR | Zbl
[24] , and , A class of location-independent variability orders, with applications. J. Appl. Probab. 47 (2010) 407–425. | DOI | MR | Zbl
[25] , Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55 (2001) 271–280. | DOI | MR | Zbl
[26] , Asymptotic Statistics. Vol. 3 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (1998). | MR | Zbl
[27] , and , Global sensitivity analysis measures the quality of parameter estimation: the case of soil parameters and a crop model. Environ. Model. Softw. 25 (2010) 310–319. | DOI
[28] , and , Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site. Stoch. Environ. Res. Risk Assess. 22 (2008) 17–31. | DOI | MR | Zbl
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