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Eliciting conditional and unconditional rank correlations from conditional probabilities

Author

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  • Morales, O.
  • Kurowicka, D.
  • Roelen, A.

Abstract

Causes of uncertainties may be interrelated and may introduce dependencies. Ignoring these dependencies may lead to large errors. A number of graphical models in probability theory such as dependence trees, vines and (continuous) Bayesian belief nets [Cooke RM. Markov and entropy properties of tree and vine-dependent variables. In: Proceedings of the ASA section on Bayesian statistical science, 1997; Kurowicka D, Cooke RM. Distribution-free continuous Bayesian belief nets. In: Proceedings of mathematical methods in reliability conference, 2004; Bedford TJ, Cooke RM. Vines—a new graphical model for dependent random variables. Ann Stat 2002; 30(4):1031–68; Kurowicka D, Cooke RM. Uncertainty analysis with high dimensional dependence modelling. New York: Wiley; 2006; Hanea AM, et al. Hybrid methods for quantifying and analyzing Bayesian belief nets. In: Proceedings of the 2005 ENBIS5 conference, 2005; Shachter RD, Kenley CR. Gaussian influence diagrams. Manage Sci 1998; 35(5) [15].] have been developed to capture dependencies between random variables. The input for these models are various marginal distributions and dependence information, usually in the form of conditional rank correlations. Often expert elicitation is required. This paper focuses on dependence representation, and dependence elicitation. The techniques presented are illustrated with an application from aviation safety.

Suggested Citation

  • Morales, O. & Kurowicka, D. & Roelen, A., 2008. "Eliciting conditional and unconditional rank correlations from conditional probabilities," Reliability Engineering and System Safety, Elsevier, vol. 93(5), pages 699-710.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:5:p:699-710
    DOI: 10.1016/j.ress.2007.03.020
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    References listed on IDEAS

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    1. 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.
    2. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
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    Cited by:

    1. Lin, P.H. & Hale, A.R. & van Gulijk, C., 2013. "A paired comparison approach to improve the quantification of management influences in air transportation," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 52-60.
    2. 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.
    3. Ale, B.J.M. & Bellamy, L.J. & van der Boom, R. & Cooper, J. & Cooke, R.M. & Goossens, L.H.J. & Hale, A.R. & Kurowicka, D. & Morales, O. & Roelen, A.L.C. & Spouge, J., 2009. "Further development of a Causal model for Air Transport Safety (CATS): Building the mathematical heart," Reliability Engineering and System Safety, Elsevier, vol. 94(9), pages 1433-1441.
    4. Hanea, Anca & Morales Napoles, Oswaldo & Ababei, Dan, 2015. "Non-parametric Bayesian networks: Improving theory and reviewing applications," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 265-284.
    5. Patrycja L. Gradowska & Roger M. Cooke, 2014. "Estimating expected value of information using Bayesian belief networks: a case study in fish consumption advisory," Environment Systems and Decisions, Springer, vol. 34(1), pages 88-97, March.
    6. Hanea, D.M. & Jagtman, H.M. & Ale, B.J.M., 2012. "Analysis of the Schiphol Cell Complex fire using a Bayesian belief net based model," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 115-124.
    7. Tim Bedford & Alireza Daneshkhah & Kevin J. Wilson, 2016. "Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 792-815, April.
    8. Morales-Nápoles, Oswaldo & Steenbergen, Raphaël D.J.M., 2014. "Analysis of axle and vehicle load properties through Bayesian Networks based on Weigh-in-Motion data," Reliability Engineering and System Safety, Elsevier, vol. 125(C), pages 153-164.
    9. Nogal, Maria & Morales Nápoles, Oswaldo & O’Connor, Alan, 2019. "Structured expert judgement to understand the intrinsic vulnerability of traffic networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 127(C), pages 136-152.
    10. Wang, Fan & Li, Heng & Dong, Chao & Ding, Lieyun, 2019. "Knowledge representation using non-parametric Bayesian networks for tunneling risk analysis," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

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