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Is eliciting dependency worth the effort? A study for the multivariate Poisson-Gamma probability model

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  • Rafael Schwarzenegger
  • John Quigley
  • Lesley Walls

Abstract

We examine whether it is worthwhile eliciting subjective judgements to account for dependency in a multivariate Poisson-Gamma probability model. The challenge of estimating reliability during product design motivated the choice of model class. For the multivariate Poisson-Gamma model we adopt an empirical Bayes methodology to present an estimator with improved accuracy. A simulation study investigates the estimation error of this estimator for different degrees of dependency and examines the impact of dependency being mis-specified when assessed by subjective judgement. Our theoretical and simulation findings give analysts insights about the value of eliciting dependency.

Suggested Citation

  • Rafael Schwarzenegger & John Quigley & Lesley Walls, 2023. "Is eliciting dependency worth the effort? A study for the multivariate Poisson-Gamma probability model," Journal of Risk and Reliability, , vol. 237(5), pages 858-867, October.
    • Handle: RePEc:sae:risrel:v:237:y:2023:i:5:p:858-867
    DOI: 10.1177/1748006X211059417
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    References listed on IDEAS

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    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. Lee, Dongjin & Pan, Rong, 2018. "A nonparametric Bayesian network approach to assessing system reliability at early design stages," Reliability Engineering and System Safety, Elsevier, vol. 171(C), pages 57-66.
    3. Hosack, Geoffrey R. & Hayes, Keith R. & Barry, Simon C., 2017. "Prior elicitation for Bayesian generalised linear models with application to risk control option assessment," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 351-361.
    4. Mkrtchyan, L. & Podofillini, L. & Dang, V.N., 2015. "Bayesian belief networks for human reliability analysis: A review of applications and gaps," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 1-16.
    5. Christoph Werner & Anca M. Hanea & Oswaldo Morales-Nápoles, 2018. "Eliciting Multivariate Uncertainty from Experts: Considerations and Approaches Along the Expert Judgement Process," International Series in Operations Research & Management Science, in: Luis C. Dias & Alec Morton & John Quigley (ed.), Elicitation, chapter 0, pages 171-210, Springer.
    6. 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.
    7. John Quigley & Lesley Walls, 2021. "Characteristics of a Process for Subjective Probability Elicitation," International Series in Operations Research & Management Science, in: Anca M. Hanea & Gabriela F. Nane & Tim Bedford & Simon French (ed.), Expert Judgement in Risk and Decision Analysis, chapter 0, pages 287-318, Springer.
    8. John Quigley & Kevin J. Wilson & Lesley Walls & Tim Bedford, 2013. "A Bayes Linear Bayes Method for Estimation of Correlated Event Rates," Risk Analysis, John Wiley & Sons, vol. 33(12), pages 2209-2224, December.
    9. John Quigley & Lesley Walls, 2018. "A Methodology for Constructing Subjective Probability Distributions with Data," International Series in Operations Research & Management Science, in: Luis C. Dias & Alec Morton & John Quigley (ed.), Elicitation, chapter 0, pages 141-170, Springer.
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