Minnesota Department of Transportation
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 of distribution of total traffic conditioned on a short count sample. This approximation is then used to derive 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% when using a two-day count sample.
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