IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v167y2017icp136-157.html
   My bibliography  Save this article

Relationship between sensitivity indices defined by variance- and covariance-based methods

Author

Listed:
  • Li, Genyuan
  • Rabitz, Herschel

Abstract

Sensitivity analysis is a challenge to perform with correlated variables, as often occur in practice. The variance-based methods for correlated variables use the same sensitivity indices defined for independent variables. The associate algorithms to determine the sensitivity indices are computationally demanding, and require explicit knowledge of the joint and conditional probability density function (pdf) of the input variables. As an alternative, a method referred to as structural and correlative sensitivity analysis (SCSA) based on a covariance decomposition has also been developed to fully quantify the deterministic and statistical contributions of independent and correlated variables, which can be applied in simulations as well as for laboratory/field data where the explicit forms of the function f(x) and the pdf are unknown. In this paper, we show that the sensitivity indices defined by the variance-based method may be re-expressed in terms of the SCSA sensitivity indices without further numerical computation, if the function f(x) and the pdf are known. If f(x) and the pdf are not known, the indices can still be accurately calculated from a single modest set of input-output data samples with SCSA.

Suggested Citation

  • Li, Genyuan & Rabitz, Herschel, 2017. "Relationship between sensitivity indices defined by variance- and covariance-based methods," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 136-157.
    • Handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:136-157
    DOI: 10.1016/j.ress.2017.05.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832016304045
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2017.05.038?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rong Liu & Lijian Yang, 2008. "Kernel estimation of multivariate cumulative distribution function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(8), pages 661-677.
    2. Jeremy E. Oakley & Anthony O'Hagan, 2004. "Probabilistic sensitivity analysis of complex models: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 751-769, August.
    3. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    4. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xie, Xiangzhong & Schenkendorf, René & Krewer, Ulrike, 2019. "Efficient sensitivity analysis and interpretation of parameter correlations in chemical engineering," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 159-173.
    2. Mara, Thierry A. & Becker, William E., 2021. "Polynomial chaos expansion for sensitivity analysis of model output with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    3. Borgonovo, Emanuele & Buzzard, Gregery T. & Wendell, Richard E., 2018. "A global tolerance approach to sensitivity analysis in linear programming," European Journal of Operational Research, Elsevier, vol. 267(1), pages 321-337.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Matieyendou Lamboni, 2020. "Uncertainty quantification: a minimum variance unbiased (joint) estimator of the non-normalized Sobol’ indices," Statistical Papers, Springer, vol. 61(5), pages 1939-1970, October.
    2. Jeffrey Racine, 2015. "Mixed data kernel copulas," Empirical Economics, Springer, vol. 48(1), pages 37-59, February.
    3. Al Ali, Hannah & Daneshkhah, Alireza & Boutayeb, Abdesslam & Malunguza, Noble Jahalamajaha & Mukandavire, Zindoga, 2022. "Exploring dynamical properties of a Type 1 diabetes model using sensitivity approaches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 324-342.
    4. Lambert, Romain S.C. & Lemke, Frank & Kucherenko, Sergei S. & Song, Shufang & Shah, Nilay, 2016. "Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 42-54.
    5. Deman, G. & Konakli, K. & Sudret, B. & Kerrou, J. & Perrochet, P. & Benabderrahmane, H., 2016. "Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 156-169.
    6. Pronzato, Luc, 2019. "Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol’ indices and experimental design," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 93-109.
    7. Touzani, Samir & Busby, Daniel, 2013. "Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 67-81.
    8. Zhang, Xufang & Pandey, Mahesh D., 2014. "An effective approximation for variance-based global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 164-174.
    9. Chen, Xin & Molina-Cristóbal, Arturo & Guenov, Marin D. & Riaz, Atif, 2019. "Efficient method for variance-based sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 97-115.
    10. Melito, Gian Marco & Müller, Thomas Stephan & Badeli, Vahid & Ellermann, Katrin & Brenn, Günter & Reinbacher-Köstinger, Alice, 2021. "Sensitivity analysis study on the effect of the fluid mechanics assumptions for the computation of electrical conductivity of flowing human blood," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    11. Matieyendou Lamboni, 2018. "Global sensitivity analysis: a generalized, unbiased and optimal estimator of total-effect variance," Statistical Papers, Springer, vol. 59(1), pages 361-386, March.
    12. Wu, Zeping & Wang, Donghui & Okolo N, Patrick & Hu, Fan & Zhang, Weihua, 2016. "Global sensitivity analysis using a Gaussian Radial Basis Function metamodel," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 171-179.
    13. Weirs, V. Gregory & Kamm, James R. & Swiler, Laura P. & Tarantola, Stefano & Ratto, Marco & Adams, Brian M. & Rider, William J. & Eldred, Michael S., 2012. "Sensitivity analysis techniques applied to a system of hyperbolic conservation laws," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 157-170.
    14. Mara, Thierry A. & Tarantola, Stefano, 2012. "Variance-based sensitivity indices for models with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 115-121.
    15. Sudret, B. & Mai, C.V., 2015. "Computing derivative-based global sensitivity measures using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 241-250.
    16. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    17. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    18. Cremona, Marzia A. & Liu, Binbin & Hu, Yang & Bruni, Stefano & Lewis, Roger, 2016. "Predicting railway wheel wear under uncertainty of wear coefficient, using universal kriging," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 49-59.
    19. Rahman, Sharif, 2011. "Global sensitivity analysis by polynomial dimensional decomposition," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 825-837.
    20. Horiguchi, Akira & Pratola, Matthew T. & Santner, Thomas J., 2021. "Assessing variable activity for Bayesian regression trees," Reliability Engineering and System Safety, Elsevier, vol. 207(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:136-157. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.