IDEAS home Printed from https://ideas.repec.org/a/spr/eurjdp/v5y2017i1d10.1007_s40070-017-0071-2.html
   My bibliography  Save this article

Sensitivity analysis of decision making under dependent uncertainties using copulas

Author

Listed:
  • Tianyang Wang

    (College of Business, Colorado State University)

  • James S. Dyer

    (University of Texas at Austin)

  • Warren J. Hahn

    (University of Texas at Austin)

Abstract

Many important decision and risk analysis problems are complicated by dependencies between input variables. In such cases, standard one-variable-at-a-time sensitivity analysis methods are typically eschewed in favor of fully probabilistic, or n-way, analysis techniques which simultaneously vary all n input variables and capture their interdependencies. Unfortunately, much of the intuition provided by one-way sensitivity analysis may not be available in fully probabilistic methods because it is difficult or impossible to isolate the marginal effects of the individual variables. In this paper, we present a dependence-adjusted approach for identifying and analyzing the impact of the input variables in a model through the use of probabilistic sensitivity analysis based on copulas. This approach provides insights about the influence of the input variables and the dependence relationships between the input variables. One contribution of this approach is that it facilitates assessment of the relative marginal influence of variables for the purpose of determining which variables should be modeled in applications where computational efficiency is a concern, such as in decision tree analysis of large-scale problems. In addition, we also investigate the sensitivity of a model to the magnitude of correlations in the inputs.

Suggested Citation

  • Tianyang Wang & James S. Dyer & Warren J. Hahn, 2017. "Sensitivity analysis of decision making under dependent uncertainties using copulas," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 117-139, November.
    • Handle: RePEc:spr:eurjdp:v:5:y:2017:i:1:d:10.1007_s40070-017-0071-2
    DOI: 10.1007/s40070-017-0071-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40070-017-0071-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40070-017-0071-2?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. Borgonovo, E., 2007. "A new uncertainty importance measure," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 771-784.
    2. Storlie, Curtis B. & Swiler, Laura P. & Helton, Jon C. & Sallaberry, Cedric J., 2009. "Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1735-1763.
    3. Athanassios N. Avramidis & Nabil Channouf & Pierre L'Ecuyer, 2009. "Efficient Correlation Matching for Fitting Discrete Multivariate Distributions with Arbitrary Marginals and Normal-Copula Dependence," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 88-106, February.
    4. Philip M. Lurie & Matthew S. Goldberg, 1998. "An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions," Management Science, INFORMS, vol. 44(2), pages 203-218, February.
    5. Tianyang Wang & James S. Dyer, 2012. "A Copulas-Based Approach to Modeling Dependence in Decision Trees," Operations Research, INFORMS, vol. 60(1), pages 225-242, February.
    6. Mark Strong & Jeremy E. Oakley, 2013. "An Efficient Method for Computing Single-Parameter Partial Expected Value of Perfect Information," Medical Decision Making, , vol. 33(6), pages 755-766, August.
    7. Luis V. Montiel & J. Eric Bickel, 2013. "Approximating Joint Probability Distributions Given Partial Information," Decision Analysis, INFORMS, vol. 10(1), pages 26-41, March.
    8. Harvey M. Wagner, 1995. "Global Sensitivity Analysis," Operations Research, INFORMS, vol. 43(6), pages 948-969, December.
    9. Manel Baucells & Emanuele Borgonovo, 2013. "Invariant Probabilistic Sensitivity Analysis," Management Science, INFORMS, vol. 59(11), pages 2536-2549, November.
    10. James C. Felli & Gordon B. Hazen, 1998. "Sensitivity Analysis and the Expected Value of Perfect Information," Medical Decision Making, , vol. 18(1), pages 95-109, January.
    11. Bahar Biller, 2009. "Copula-Based Multivariate Input Models for Stochastic Simulation," Operations Research, INFORMS, vol. 57(4), pages 878-892, August.
    12. Ingram Olkin, 1981. "Range restrictions for product-moment correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 469-472, December.
    13. Robert T. Clemen & Gregory W. Fischer & Robert L. Winkler, 2000. "Assessing Dependence: Some Experimental Results," Management Science, INFORMS, vol. 46(8), pages 1100-1115, August.
    14. Kousky, Carolyn & Cooke, Roger M., 2009. "The Unholy Trinity: Fat Tails, Tail Dependence, and Micro-Correlations," RFF Working Paper Series dp-09-36-rev.pdf, Resources for the Future.
    15. E. Borgonovo & C. L. Smith, 2011. "A Study of Interactions in the Risk Assessment of Complex Engineering Systems: An Application to Space PSA," Operations Research, INFORMS, vol. 59(6), pages 1461-1476, December.
    16. Akshay Mutha & Saurabh Bansal & V. Daniel R. Guide, 2016. "Managing Demand Uncertainty through Core Acquisition in Remanufacturing," Production and Operations Management, Production and Operations Management Society, vol. 25(8), pages 1449-1464, August.
    17. 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.
    18. 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.
    19. James C. Felli & Gordon B. Hazen, 2004. "Javelin Diagrams: A Graphical Tool for Probabilistic Sensitivity Analysis," Decision Analysis, INFORMS, vol. 1(2), pages 93-107, June.
    20. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
    21. Luis V. Montiel & J. Eric Bickel, 2012. "A Simulation-Based Approach to Decision Making with Partial Information," Decision Analysis, INFORMS, vol. 9(4), pages 329-347, December.
    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. Hasanain A. H. Al-Hilfi & Ahmed Abu-Siada & Farhad Shahnia, 2020. "Combined ANFIS–Wavelet Technique to Improve the Estimation Accuracy of the Power Output of Neighboring PV Systems during Cloud Events," Energies, MDPI, vol. 13(7), pages 1-15, April.
    2. Lu, Xuefei & Borgonovo, Emanuele, 2023. "Global sensitivity analysis in epidemiological modeling," European Journal of Operational Research, Elsevier, vol. 304(1), pages 9-24.

    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. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    2. S. Cucurachi & E. Borgonovo & R. Heijungs, 2016. "A Protocol for the Global Sensitivity Analysis of Impact Assessment Models in Life Cycle Assessment," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 357-377, February.
    3. Emanuele Borgonovo & Gordon B. Hazen & Elmar Plischke, 2016. "A Common Rationale for Global Sensitivity Measures and Their Estimation," Risk Analysis, John Wiley & Sons, vol. 36(10), pages 1871-1895, October.
    4. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    5. Tianyang Wang & James S. Dyer, 2012. "A Copulas-Based Approach to Modeling Dependence in Decision Trees," Operations Research, INFORMS, vol. 60(1), pages 225-242, February.
    6. 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.
    7. Gordon Hazen & Emanuele Borgonovo & Xuefei Lu, 2023. "Information Density in Decision Analysis," Decision Analysis, INFORMS, vol. 20(2), pages 89-108, June.
    8. Tianyang Wang & James S. Dyer & John C. Butler, 2016. "Modeling Correlated Discrete Uncertainties in Event Trees with Copulas," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 396-410, February.
    9. Borgonovo, Emanuele & Hazen, Gordon B. & Jose, Victor Richmond R. & Plischke, Elmar, 2021. "Probabilistic sensitivity measures as information value," European Journal of Operational Research, Elsevier, vol. 289(2), pages 595-610.
    10. Manel Baucells & Emanuele Borgonovo, 2013. "Invariant Probabilistic Sensitivity Analysis," Management Science, INFORMS, vol. 59(11), pages 2536-2549, November.
    11. Pesenti, Silvana M. & Millossovich, Pietro & Tsanakas, Andreas, 2019. "Reverse sensitivity testing: What does it take to break the model?," European Journal of Operational Research, Elsevier, vol. 274(2), pages 654-670.
    12. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
    13. Konakli, Katerina & Sudret, Bruno, 2016. "Global sensitivity analysis using low-rank tensor approximations," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 64-83.
    14. Emanuele Borgonovo & Marco Pangallo & Jan Rivkin & Leonardo Rizzo & Nicolaj Siggelkow, 2022. "Sensitivity analysis of agent-based models: a new protocol," Computational and Mathematical Organization Theory, Springer, vol. 28(1), pages 52-94, March.
    15. Tatsuya Sakurahara & Seyed Reihani & Ernie Kee & Zahra Mohaghegh, 2020. "Global importance measure methodology for integrated probabilistic risk assessment," Journal of Risk and Reliability, , vol. 234(2), pages 377-396, April.
    16. 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.
    17. Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
    18. Lu, Xuefei & Borgonovo, Emanuele, 2023. "Global sensitivity analysis in epidemiological modeling," European Journal of Operational Research, Elsevier, vol. 304(1), pages 9-24.
    19. Ge, Qiao & Menendez, Monica, 2017. "Extending Morris method for qualitative global sensitivity analysis of models with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 162(C), pages 28-39.
    20. 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.

    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:spr:eurjdp:v:5:y:2017:i:1:d:10.1007_s40070-017-0071-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.