A kernel density empirical Bayes (KDEB) approach to estimate accident risk

We propose the kernel density empirical Bayes (KDEB) approach as an improvement to the kernel density estimate (KDE) approach to the analysis of crash data. The KDEB estimates the crash risk at a road section as the weighted average of the KDE and the crash count. The KDE optimal bandwidth and the weight are simultaneously determined by minimizing an unbiased estimate of the mean square error of the estimated crash risk and the true unknown crash risk. Furthermore, the KDEB can take into account the temporal variation of crash risk. Simulation examples and crash count data from two interstate roads are used to illustrate the KDEB approach. Because of the empirical Bayes approach incorporated in the KDEB, the KDEB separates the smooth spatial variation of the crash risk from the random spatial variation giving a more robust interpretation of the crash risk. Incorporating the temporal variation results in a smaller mean square error in the case of the simulated example and a smaller mean square prediction error in the case of the crash data example. Therefore, incorporating temporal variation better addresses the problem of regression to the mean bias which guards against overestimating the effect of potential safety countermeasures.