IDEAS home Printed from
   My bibliography  Save this article

Sensitivity analysis of decision making under dependent uncertainties using copulas


  • 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

    Download full text from publisher

    File URL:
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

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

    References listed on IDEAS

    1. repec:eee:reensy:v:92:y:2007:i:6:p:771-784 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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.
    5. Luis V. Montiel & J. Eric Bickel, 2013. "Approximating Joint Probability Distributions Given Partial Information," Decision Analysis, INFORMS, vol. 10(1), pages 26-41, March.
    6. Harvey M. Wagner, 1995. "Global Sensitivity Analysis," Operations Research, INFORMS, vol. 43(6), pages 948-969, December.
    7. Manel Baucells & Emanuele Borgonovo, 2013. "Invariant Probabilistic Sensitivity Analysis," Management Science, INFORMS, vol. 59(11), pages 2536-2549, November.
    8. Bahar Biller, 2009. "Copula-Based Multivariate Input Models for Stochastic Simulation," Operations Research, INFORMS, vol. 57(4), pages 878-892, August.
    9. Ingram Olkin, 1981. "Range restrictions for product-moment correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 469-472, December.
    10. 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.
    11. Kousky, Carolyn & Cooke, Roger M., 2009. "The Unholy Trinity: Fat Tails, Tail Dependence, and Micro-Correlations," Discussion Papers dp-09-36-rev.pdf, Resources For the Future.
    12. 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.
    13. 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.
    14. repec:eee:reensy:v:107:y:2012:i:c:p:115-121 is not listed on IDEAS
    15. 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.
    16. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
    17. 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)


    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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.