Parametric Empirical Bayes Estimates of Truck Accident Rates

Abstract

The two common approaches to estimation of truck accident rates are an aggregate method, in which the data from all available road segments are pooled, and a segment-specific method, in which separate accident-rate estimates are obtained for each road segment. The aggregate method benefits from the use of a relatively large data set, but fails to capture the variation across road segments that can potentially be measured with the segment specific approach. In this paper, we describe an empirical Bayes procedure for obtaining reliable accident-rate estimates through use of an optimal compromise between the aggregate and the segment-specific estimation methods. We then examine two methods of determining accident probabilities from the empirical Bayes accident rates, an approximate method and an exact method. The empirical Bayes technique is applied to accident data from a regional network in northeast Ohio. Results show that the Bayes estimator behaves rationally; the estimates tend to balance the prior aggregate beliefs with segment-specific data while maintaining continuity between what were previously two separate estimation philosophies.