Estimating rate of occurrence of rare events with empirical Bayes: a railway application

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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. This paper considers the application of Empirical Bayes to high consequence low-frequency events, where estimates are required for risk mitigation decision support such as as low as reasonably possible. A summary of empirical Bayes methods is given and the choices of estimation procedures to obtain interval estimates are discussed. The approaches illustrated within the case study are based on the estimation of the rate of occurrence of train derailments within the UK. The usefulness of empirical Bayes within this context is discussed
LanguageEnglish
Pages619-627
Number of pages8
JournalReliability Engineering and System Safety
Volume92
Issue number5
DOIs
Publication statusPublished - May 2007

Fingerprint

Empirical Bayes
Rare Events
Railway
Point Estimate
Derailments
Empirical Bayes Method
Bayes Procedures
Maximum likelihood
Noninformative Prior
Hazards
Pooling
Alternatives
Zero
Prior distribution
Decision Support
Statistical Inference
Hazard
Maximum Likelihood Estimator
Estimate
Low Frequency

Keywords

  • rare events
  • empirical Bayes
  • railway
  • reliability engineering
  • system safety
  • credibility theory
  • zero failure
  • estimation
  • homogeneous Poisson process

Cite this

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title = "Estimating rate of occurrence of rare events with empirical Bayes: a railway application",
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. This paper considers the application of Empirical Bayes to high consequence low-frequency events, where estimates are required for risk mitigation decision support such as as low as reasonably possible. A summary of empirical Bayes methods is given and the choices of estimation procedures to obtain interval estimates are discussed. The approaches illustrated within the case study are based on the estimation of the rate of occurrence of train derailments within the UK. The usefulness of empirical Bayes within this context is discussed",
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