A Bayesian Hierarchical Approach to Model the Rank of Hazardous Intersections for Bicyclists using the Gibbs Sampler

Abstract

In this paper, Bayesian hierarchical modeling techniques are used to identify and rank hazardous intersections for bicycles in Leuven, a small university town in Belgium. The objective of this paper is to infer the process of listing the most dangerous intersections, based on the available accident data. The hierarchical random effects model allows the specification of different sources of variation, namely the variation between intersections and the variation within each intersection. The Gibbs sampler is used to explore the distribution of the bicycle accident proportions. An important advantage of the Gibbs sampler is the possibility to sample complex functions of the bicycle accident proportions, like the rank of an intersection. It is shown that the ranking itself could be seen as a density. Since the bicycle accident proportions have a stochastic character, the ranking of intersections based on the mean posterior proportion cannot be deterministic. Ranking hazardous sites is an interesting means to get insight in dangerous locations, but there is no such thing as “the” correct ranking. This paper investigates the question whether a ranking alone can give enough evidence for the selection of dangerous sites.