An application of copulas to accident precursor analysis

Data on accident precursors can help in estimating accident frequencies, si nce they provide a rich source of information on intersystem dependencies. However, Bayesian analysis of accident precursors requires the ability to c onstruct joint prior distributions reflecting such dependencies. For exampl e, the failure probabilities of a particular safety system under normal and accident conditions, respectively, will generally not be identical (becaus e of the effects of the accident), but will almost certainly be correlated (since both failure probabilities reflect the performance of the same compo nents, with the same inherent levels of reliability). In this paper, we exp lore the use of copulas (a method of representing joint distribution functi ons with particular marginals) to construct the needed prior distributions, and then use these distributions in a Bayesian analysis of hypothetical pr ecursor data. This demonstrates the usefulness of copulas in practice. The same approach can also be used in a wide variety of other contexts where jo int distributions with particular marginals are desired.