Software
The Risk Consortium appreciates the importance of software to support decision-making and to communicate clearly different theoretical methods. Currently, the Risk Consortium has developed two Excel-based tools that allow practitioners to automatically carry out complex calculations.
Empirical Bayes Analysis
Classical methods to estimate the rate of occurrence for rare events typically perform poorly. These methods use the ratio between events and duration of operation to give an unbiased estimator of the rate of occurrence. However, where few data exists, there is a relatively high probability of the estimate being zero. This is obviously inappropriate for most cases.
Empirical Bayes methods pool data from various events together to estimate an overall rate and then adjust this overall rate for each individual event. Empirical Bayes differs from Bayesian methods as they pool data to estimate the prior distribution and, therefore, do not utilise subjective expert judgement.
For more information, see Quigley J, Bedford T and Walls L, Estimating rate of occurrence of rare events with Empirical Bayes: A railway application (2007) Reliability Engineering and System Safety 92 619-627.
The Empirical Bayes Software simplifies the Empirical Bayes process by calculating the parameters of the pooled distribution and updating the point estimates based on the Empirical Bayes formulas. The software also compares the Empirical Bayes estimate to the classical estimate. In addition, the software also calculates confidence intervals for all the estimates.
Bayes Linear Analysis
The Bayes linear methodology is a quantitative method to express subjective beliefs and to update these beliefs once observations have been made. It is an inferential tool that is similar in philosophy to "standard" probabilistic Bayesian methods but has a number of distinct features which give it certain advantages over the standard approach when modelling complex problems. While “standard” Bayesian approaches are demanding in terms of time, computational and elicitation effort, the Bayes linear methodology offers a relatively quick and simple method to perform inference using mathematical expectation rather than probability as a basis. As such, the elicitation specification required from a decision maker is reduced and hence more complex scenarios can be modelled for an equivalent amount of resource.
For further information on Bayes Linear, see Revie, Matthew (2007) Evaluation of Bayes Linear Modelling to Support Reliability Assessment During Procurement, PhD Thesis, University of Strathclyde.
