Estimation of high consequence low frequency events through Empirical Bayes procedures

摘要

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.rnWe consider the application of such procedures to high consequence low frequency events, where estimates are required for risk mitigation decision support, such as ALARP. In particular, we consider supporting inference for the rate of occurrence of derailments within the UK, where the Railway Safety and Standard Board assess risk through an elaborate fault and event tree. The model consists of 68 base events with 66 derailments from which to support inference.rnThis paper presents a summary of Empirical Bayes methods and provides a discussion on the choices of estimation procedures to obtain interval estimates. The methods are illustrated with the case study.