IDEAS home Printed from
   My bibliography  Save this article

Probabilistic Inversion of Expert Judgments in the Quantification of Model Uncertainty


  • Bernd Kraan

    () (Department of Information, Technology and Systems, Delft University of Technology, CROSS, Mekelweg 4, 2628 CD Delft, The Netherlands, and Risk and Uncertainty Management (RandUM), Plein Delftzicht 51, 2627 CA Delft, The Netherlands)

  • Tim Bedford

    () (Department of Management Science, Strathclyde Business School, University of Strathclyde, 40 George Street, Glasgow G1 1QE, Scotland)


Expert judgment is frequently used to assess parameter values of quantitative management science models, particularly in decision-making contexts. Experts can, however, only be expected to assess observable quantities, not abstract model parameters. This means that we need a method for translating expert assessed uncertainties on model outputs into uncertainties on model parameter values. This process is called probabilistic inversion. The probability distribution on model parameters obtained in this way can be used in a variety of ways, but in particular in an uncertainty analysis or as a Bayes prior. This paper discusses computational algorithms that have proven successful in various projects and gives examples from environmental modelling and banking. Those algorithms are given a theoretical basis by adopting a minimum information approach to modelling partial information. The role of minimum information is two-fold: It enables us to resolve the problem of nonuniqueness of distributions given the information we have, and it provides numerical stability to the algorithm by guaranteeing convergence properties.

Suggested Citation

  • Bernd Kraan & Tim Bedford, 2005. "Probabilistic Inversion of Expert Judgments in the Quantification of Model Uncertainty," Management Science, INFORMS, vol. 51(6), pages 995-1006, June.
  • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:6:p:995-1006

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Miller, Douglas J. & Liu, Wei-han, 2002. "On the recovery of joint distributions from limited information," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 259-274, March.
    2. Zellner, Arnold, 2002. "Information processing and Bayesian analysis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 41-50, March.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    2. repec:eee:reensy:v:136:y:2015:i:c:p:35-46 is not listed on IDEAS
    3. repec:eee:reensy:v:125:y:2014:i:c:p:3-12 is not listed on IDEAS
    4. Chen Wang & Vicki M. Bier, 2013. "Expert Elicitation of Adversary Preferences Using Ordinal Judgments," Operations Research, INFORMS, vol. 61(2), pages 372-385, April.
    5. repec:eee:reensy:v:96:y:2011:i:9:p:1076-1084 is not listed on IDEAS
    6. repec:eee:reensy:v:93:y:2008:i:5:p:657-674 is not listed on IDEAS
    7. Ríos Insua, David & Cano, Javier & Pellot, Michael & Ortega, Ricardo, 2016. "Multithreat multisite protection: A security case study," European Journal of Operational Research, Elsevier, vol. 252(3), pages 888-899.
    8. repec:eee:reensy:v:133:y:2015:i:c:p:59-67 is not listed 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:inm:ormnsc:v:51:y:2005:i:6:p:995-1006. 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: (Mirko Janc). 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.