Empirical Bayesian analysis of accident severity for motorcyclists in large French urban areas

The present article deals with individual probabilities of different levels of injury in case of a motorcycle accident. The approach uses an empirical Bayesian method based on the Multinomial-Dirichlet model, see [Leonard, T., 1977. A Bayesian approach to some Multinomial estimation and pretesting problems, J. Am. Stat. Association, 72, 869–874], to conduct an analysis of the probability distributions about the severity of accidents at the level of individuals in large and dense French urban areas during year 2003. We model accident severity using four levels of injury: material damages only, slight injury, severe injury, fatal injury. Our application shows that sociodemographic characteristics of motorcyclists and factors influencing their speed behaviors, the suddenness of their collision and the vigilance of road users play significant roles on the shapes of their probability distributions of accident severity. The computation of posterior distributions of the levels of injury for different groups of motorcyclists enables us to rank them with respect to their risk of injury using second order stochastic dominance orderings. It is found that women motorcyclists between 30 and 50 years old driving powerful motorcycles are the most exposed to risk of injury.