Estimating traffic accident rates while accounting for traffic-volume estimation error: A Gibbs sampling approach

Traffic-accident rates that are estimated for individual roadway sites are often used to identify potentially hazardous locations. Occasionally they are used to test whether an accident countermeasure is associated with a statistically significant change in accident rate. In assessing the uncertainty attached to estimated accident rates, it is often implicitly assumed that the total traffic at a site is known with certainty, when in actuality the total traffic almost always must be estimated from a short sample of traffic counts. This introduces estimation error, which, if ignored can lead one to overstate the accuracy of an accident-rate estimate. An explanation is provided about how Bayes estimates of accident rates, which explicitly account for total traffic estimation error, can be computed readily using a (relatively) new estimation method called "Gibbs sampling." A model of how traffic-count samples are related to total traffic is incorporated from earlier work done by the author and his students. In tests conducted using accident counts and traffic data from 17 automatic traffic-recorder sites in Minnesota, it was found that, when using a 2-day traffic-count sample, the traditional method for estimating accidents rates understated the likely error of these estimates by 12 to 40 percent, depending on the site.