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Probabilistic Inversion of Expert Judgments in the Quantification of Model Uncertainty

Author

Listed:
  • 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)

Abstract

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
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    File URL: http://dx.doi.org/10.1287/mnsc.1050.0370
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    References listed on IDEAS

    as
    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.
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    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. repec:eee:reensy:v:96:y:2011:i:9:p:1076-1084 is not listed on IDEAS
    5. repec:eee:reensy:v:93:y:2008:i:5:p:657-674 is not listed on IDEAS
    6. 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.
    7. repec:eee:reensy:v:133:y:2015:i:c:p:59-67 is not listed on IDEAS

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