Computation of the Sobol' Indices using importance sampling

Pierre Beaurepaire; Matteo Broggi; Edoardo Patelli

doi:10.1061/9780784413609.212

Computation of the Sobol' Indices using importance sampling

Pierre Beaurepaire, Matteo Broggi, Edoardo Patelli

Civil And Environmental Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

2 Citations (Scopus)

Abstract

The contribution of uncertain parameters to the variability of a model may be estimated by means of global sensitivity analysis. The use of the first order Sobol' indices is relevant in this context. However, accurate estimation of these coefficients may be a challenging problem, since as many Monte Carlo simulations as the dimension of the input parameters of the problem have to be performed in order to compute all the first order Sobol' indices. Such numerical efforts are not practicable for many large scale applications. This paper presents a novel procedure which requires to perform a single Monte Carlo simulation to determine all the Sobol' indices associated with the input parameters. The benefits of the method are illustrated with an application example.

Original language	English
Title of host publication	Vulnerability, Uncertainty, and Risk
Subtitle of host publication	Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014
Editors	Jim W. Hall, Siu-Kui Au, Michael Beer
Publisher	American Society of Civil Engineers (ASCE)
Pages	2115-2124
Number of pages	10
ISBN (Electronic)	9780784413609
DOIs	https://doi.org/10.1061/9780784413609.212
Publication status	Published - 7 Jul 2014
Event	2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014 - Liverpool, United Kingdom Duration: 13 Jul 2014 → 16 Jul 2014

Publication series

Name	Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014

Conference

Conference	2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014
Country/Territory	United Kingdom
City	Liverpool
Period	13/07/14 → 16/07/14

Keywords

computing in civil engineering
sensitivity analysis
variance-based sensitivity
uncertainty analysis
importance sampling
intelligent systems
Monte Carlo methods
parameter estimation
risk analysis
risk assessment

Access to Document

10.1061/9780784413609.212

Cite this

Beaurepaire, P., Broggi, M., & Patelli, E. (2014). Computation of the Sobol' Indices using importance sampling. In J. W. Hall, S.-K. Au, & M. Beer (Eds.), Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014 (pp. 2115-2124). (Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014). American Society of Civil Engineers (ASCE). https://doi.org/10.1061/9780784413609.212

Beaurepaire, Pierre ; Broggi, Matteo ; Patelli, Edoardo. / Computation of the Sobol' Indices using importance sampling. Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014. editor / Jim W. Hall ; Siu-Kui Au ; Michael Beer. American Society of Civil Engineers (ASCE), 2014. pp. 2115-2124 (Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014).

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title = "Computation of the Sobol' Indices using importance sampling",

abstract = "The contribution of uncertain parameters to the variability of a model may be estimated by means of global sensitivity analysis. The use of the first order Sobol' indices is relevant in this context. However, accurate estimation of these coefficients may be a challenging problem, since as many Monte Carlo simulations as the dimension of the input parameters of the problem have to be performed in order to compute all the first order Sobol' indices. Such numerical efforts are not practicable for many large scale applications. This paper presents a novel procedure which requires to perform a single Monte Carlo simulation to determine all the Sobol' indices associated with the input parameters. The benefits of the method are illustrated with an application example.",

keywords = "computing in civil engineering, sensitivity analysis, variance-based sensitivity, uncertainty analysis, importance sampling, intelligent systems, Monte Carlo methods, parameter estimation, risk analysis, risk assessment",

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Beaurepaire, P, Broggi, M & Patelli, E 2014, Computation of the Sobol' Indices using importance sampling. in JW Hall, S-K Au & M Beer (eds), Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014. Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014, American Society of Civil Engineers (ASCE), pp. 2115-2124, 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014, Liverpool, United Kingdom, 13/07/14. https://doi.org/10.1061/9780784413609.212

Computation of the Sobol' Indices using importance sampling. / Beaurepaire, Pierre; Broggi, Matteo; Patelli, Edoardo.
Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014. ed. / Jim W. Hall; Siu-Kui Au; Michael Beer. American Society of Civil Engineers (ASCE), 2014. p. 2115-2124 (Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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KW - variance-based sensitivity

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T3 - Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014

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Beaurepaire P, Broggi M, Patelli E. Computation of the Sobol' Indices using importance sampling. In Hall JW, Au SK, Beer M, editors, Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014. American Society of Civil Engineers (ASCE). 2014. p. 2115-2124. (Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of the 2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014). doi: 10.1061/9780784413609.212

Computation of the Sobol' Indices using importance sampling

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