Risk analysis using a hybrid Bayesian-approximate reasoning methodology

Analysts are sometimes asked to make frequency estimates for specific accidents in which the accident frequency is determined primarily by safety controls. Under these conditions, frequency estimates use considerable expert belief in determining how the controls affect the accident frequency. To evaluate and document beliefs about control effectiveness, they have modified a traditional Bayesian approach by using approximate reasoning (AR) to develop prior distributions. Their method produces accident frequency estimates that separately express the probabilistic results produced in Bayesian analysis and possibilistic results that reflect uncertainty about the prior estimates. Based on their experience using traditional methods, they feel that the AR approach better documents beliefs about the effectiveness of controls than if the beliefs are buried in Bayesian prior distributions. They have performed numerous expert elicitations in which probabilistic information was sought from subject matter experts not trained in probability. They find it much easier to elicit the linguistic variables and fuzzy set membership values used in AR than to obtain the probability distributions used in prior distributions directly from these experts because it better captures their beliefs and better expresses their uncertainties