Improving traffic safety is a priority of Departments of Transportation nationwide. Because every agency faces budgetary constraints, methods to identify those sites with the highest risk potential and that may respond to interventions are of special importance. The initial objective of this work is to develop an accurate approach that can be used to construct candidate lists of intersections for improvement. To do so, the methodology must take into account not only the estimated expected crash frequency (or crash rate) but also the uncertainties associated with that estimate.

After focusing on the inclusion of covariates and specific ranking methods, we add a multivariate component to our Poisson/Gamma model to account for different crash severities (i.e., fatal, injury, property damage only). Simultaneously modeling different severities preserves the correlation structure in the data and also allows for borrowing strength between different severity types (i.e., we are able to model rarely occurring fatal crashes with less uncertainty and bias than in the univariate case). In contrast to many other authors, we introduce a model that allows for two- and three-way covariance structures.

Lastly, we use a Poisson Markov random field (PMRF) approach to introduce spatial dependence into our framework. While this allows for directly modeling dependence on the data level, it introduces computational challenges for estimating model parameters within the Bayesian framework. This is due to the presence of potentially intractable normalizing constants in the joint posterior distribution. We use approximate Bayesian computation (ABC) and develop algorithms to perform parameter estimation via ABC in a PMRF model.