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Probabilistic Inversion of Expert Judgments in the Quantification of Model Uncertainty

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  • 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
    DOI: 10.1287/mnsc.1050.0370
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    References listed on IDEAS

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    1. Zellner, Arnold, 2002. "Information processing and Bayesian analysis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 41-50, March.
    2. 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.
    3. Craig P. S & Goldstein M. & Rougier J. C & Seheult A. H, 2001. "Bayesian Forecasting for Complex Systems Using Computer Simulators," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 717-729, June.
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    Cited by:

    1. Bier, Vicki M. & Kosanoglu, Fuat, 2015. "Target-oriented utility theory for modeling the deterrent effects of counterterrorism," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 35-46.
    2. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    3. Bedford, Tim & Wilson, Kevin J. & Daneshkhah, Alireza, 2014. "Assessing parameter uncertainty on coupled models using minimum information methods," Reliability Engineering and System Safety, Elsevier, vol. 125(C), pages 3-12.
    4. Ioanna Ioannou & Jaime E. Cadena & Willy Aspinall & David Lange & Daniel Honfi & Tiziana Rossetto, 2022. "Prioritization of hazards for risk and resilience management through elicitation of expert judgement," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 112(3), pages 2773-2795, July.
    5. Cooke, Roger M. & Goossens, Louis L.H.J., 2008. "TU Delft expert judgment data base," Reliability Engineering and System Safety, Elsevier, vol. 93(5), pages 657-674.
    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. de Jonge, Bram & Klingenberg, Warse & Teunter, Ruud & Tinga, Tiedo, 2015. "Optimum maintenance strategy under uncertainty in the lifetime distribution," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 59-67.
    8. 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.
    9. R. E. J. Neslo & W. Oei & M. P. Janssen, 2017. "Insight into “Calculated Risk”: An Application to the Prioritization of Emerging Infectious Diseases for Blood Transfusion Safety," Risk Analysis, John Wiley & Sons, vol. 37(9), pages 1783-1795, September.
    10. Chen Wang & Vicki M. Bier, 2013. "Expert Elicitation of Adversary Preferences Using Ordinal Judgments," Operations Research, INFORMS, vol. 61(2), pages 372-385, April.
    11. Wilson, Alyson G. & Anderson-Cook, Christine M. & Huzurbazar, Aparna V., 2011. "A case study for quantifying system reliability and uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1076-1084.
    12. Kosanoglu, Fuat & Bier, Vicki M., 2020. "Target-oriented utility for interdiction of transportation networks," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    13. Christoph Werner & Tim Bedford & John Quigley, 2018. "Sequential Refined Partitioning for Probabilistic Dependence Assessment," Risk Analysis, John Wiley & Sons, vol. 38(12), pages 2683-2702, December.

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