Empirical Bayes approach to the estimation of "unsafety": the multivariate regression method

There are two kinds of clues to the unsafety of an entity: its traits (such as traffic, geometry, age, or gender) and its historical accident record. The Empirical Bayes approach to unsafety estimation makes use of both kinds of clues. It requires information about the mean and the variance of the unsafety in a "reference population" of similar entities. The method now in use for this purpose suffers from several shortcomings. First, a very large reference population is required. Second, the choice of reference population is to some extent arbitrary. Third, entities in the reference population usually cannot match the traits of the entity the unsafety of which is estimated. To alleviate these shortcomings the multivariate regression method for estimating the mean and variance of unsafety in reference populations is offered. Its logical foundations are described and its soundness is demonstrated. The use of the multivariate method makes the Empirical Bayes approach to unsafety estimation applicable to a wider range of circumstances and yields better estimates of unsafety. The application of the method to the tasks of identifying deviant entities and of estimating the effect of interventions on unsafety are discussed and illustrated by numerical examples.