Empirical Bayes methods to support risk analysis
Classical estimates of risk use observed data and, especially when sample sizes are small, errors in the estimates obtained can be large. An alternative approach to classical estimation is to use methods which rely on subjective assessments, such as Bayesian methods.
Bayesian methods require considerable problem structuring to assess uncertainties with all possible events. Experts are required to describe their uncertainty through subjective probability distributions, referred to as the prior distribution, as it is prior to observing the data. While problem structuring can be beneficial since insights gained can inform qualitative risk assessment, the quantification of an expert’s uncertainty can result in a significant cognitive burden and so needs to be managed with care.
Bayesian priors are usually constructed from subjective beliefs about the value of an event probability, empirical Bayes provides a means of pooling observed data from various sources related to heritage systems to form an empirical prior. Such pooling methods increase sample size and reduce error in estimation.
- A Bayes linear Bayes method for estimation of correlated event rates
- Mixing Bayes and empirical Bayes inference to anticipate the realization of engineering concerns about variant system designs
- Merging expert and empirical data for rare event frequency estimation: pool homogenisation for empirical Bayes models
- Empirical bayes estimates of development reliability for one shot devices
- Estimating rate of occurrence of rare events with empirical Bayes: a railway application