Development And Testing Of Methods For Estimating The Impact of Safety Improvements

This report describes a Bayesian method for estimating accident rates at individual sites, which takes into account the fact that the total traffic count usually used to measure exposure is generally not known with certainty. The first step involves deriving an approximation for the probability distribution of total traffic conditioned on a short count sample. This approximation is then used to drive a Bayes estimator of a site's accident rate, conditioned on an accident count, a short count sample, and the total traffic approximation. The method then uses Gibbs sampling to compute accident rate estimates. Tests based on actual accident and traffic data revealed that accident rate estimates based on a two-week traffic sample area are almost as accurate as estimates based on full traffic counting, but that uncertainty in the estimated accident rates increase by 20 to 50 percent when using a two-day count sample. This report represents the results of research conducted by the author and does not necessarily represent the views or policies of the Minnesota Department of Transportation. This report does not contain a standard or specified technique. Bouzarjomehri and Loren Hill, for providing the data used in this project. The author would also like to thank Chen Wei for processing the accident data, and Shimin Yang for conducting the evaluation of the total traffic predictions. This report deals with the problem of estimating the accident rate at a specified roadway site when the total traffic at the site is not known with certainty, by must be estimated from a traffic count sample. Although the standard statistical methods for estimating accidents rates implicitly assume that total traffic is known, in almost all practical cases this is not so. Neglecting the additional uncertainty arising from estimating the total traffic can lead to falsely identifying a site as a potential high-hazard location, or to falsely concluding that a safety treatment has had a significant effect on accident occurrence. After briefly reviewing standard practice in accident rate estimation, it is argued that a Bayesian approach to statistical inference more nearly matches the requirements and expectations of safety engineers. Consideration of accident rate estimation reveals that standard methods in essence use the sample to compute a heuristic prediction of total traffic, but that no formal treatment of this prediction problem has been done. Chapter 2 provides this treatment, and builds on earlier work by the PI to develop a Bayesian …