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Estimating rate of occurrence of rare events with empirical bayes: A railway application

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  • Quigley, John
  • Bedford, Tim
  • Walls, Lesley

Abstract

Classical approaches to estimating the rate of occurrence of events perform poorly when data are few. Maximum likelihood estimators result in overly optimistic point estimates of zero for situations where there have been no events. Alternative empirical-based approaches have been proposed based on median estimators or non-informative prior distributions. While these alternatives offer an improvement over point estimates of zero, they can be overly conservative. Empirical Bayes procedures offer an unbiased approach through pooling data across different hazards to support stronger statistical inference.

Suggested Citation

  • Quigley, John & Bedford, Tim & Walls, Lesley, 2007. "Estimating rate of occurrence of rare events with empirical bayes: A railway application," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 619-627.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:5:p:619-627
    DOI: 10.1016/j.ress.2006.02.007
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    References listed on IDEAS

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    1. Vaurio, Jussi K. & Jänkälä, Kalle E., 2006. "Evaluation and comparison of estimation methods for failure rates and probabilities," Reliability Engineering and System Safety, Elsevier, vol. 91(2), pages 209-221.
    2. Vaurio, Jussi K., 2005. "Uncertainties and quantification of common cause failure rates and probabilities for system analyses," Reliability Engineering and System Safety, Elsevier, vol. 90(2), pages 186-195.
    3. Bühlmann, Hans, 1967. "Experience Rating and Credibility," ASTIN Bulletin, Cambridge University Press, vol. 4(3), pages 199-207, July.
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    Cited by:

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    7. Quigley, John & Walls, Lesley, 2011. "Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 933-941.
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    10. Nima Khakzad & Faisal Khan & Paul Amyotte, 2015. "Major Accidents (Gray Swans) Likelihood Modeling Using Accident Precursors and Approximate Reasoning," Risk Analysis, John Wiley & Sons, vol. 35(7), pages 1336-1347, July.
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    13. Quigley, John & Hardman, Gavin & Bedford, Tim & Walls, Lesley, 2011. "Merging expert and empirical data for rare event frequency estimation: Pool homogenisation for empirical Bayes models," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 687-695.

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