6. Probability and plausibility

The debate between the two primary schools of probability, frequentist and Bayesian, has of course been going on for over a couple of centuries. Both have their shortcomings when applied to safety.

For example, the frequentist approach applies to large numbers of events and a frequentist probability is a prediction of how often something is expected to occur over a number of opportunities for it to occur. Using frequentist statistics and associated probabilities requires a subjective decision about significance levels (that is, when do you take a result seriously), and they require enough relevant events to indicate a trend. Obviously, when there’s a surprising accident or serious incident, it’s not in the interest of safety to wait for a significant trend to emerge.

In contrast, a Bayesian approach is better suited to rare events. While a Bayesian analysis would do a better job of incorporating and learning from smaller numbers of new events, updating a prior probability requires that there be a prior probability in the first place, which is also necessarily subjective when dealing with rare events. In other words, one has to have a theory and be willing to update it based on new evidence.

According to Aubrey Clayton (Bernoulli’s Fallacy), recent attempts to reconcile the two schools have focused on the notion of “plausibility”. He summarizes this work by saying that “probability is best understood as the plausibility of some event given some assumed information”. Note that plausibility can apply equally well to expectations about the frequency of occurrence and about the likelihood of single outcomes.

I think this is a good construct to use in safety analyses of rare events, and that the safety-related standards and literature already tacitly use it. For example, the global airworthiness regulations refer to “any foreseeable operating condition” and “reasonably expected”, which are just other ways of saying plausible.

And I think it’s particularly useful when dealing with human-related risks because it helps bound the analysis space. Human behavior is typically not random. While it is highly variable and impractical to predict, it’s at least systematically related to the combination of human characteristics and circumstances. The whole field of human factors has been dedicated to understanding these relationships, so human factors can help us separate plausible scenarios and outcomes from those that are implausible.