Bayesian hierarchical modeling of the non-stationary traffic conflict extremes for crash estimation

A Bayesian hierarchical modeling (BHM) approach is used to model non-stationary traffic conflict extremes of different sites together for crash estimation. The hierarchical structure has three layers, a data layer that is modeled with a generalized extreme value (GEV) distribution, a latent Gaussian process layer that relates parameters of GEV to covariates and the unobserved heterogeneity, and a prior layer with prior distributions to characterize the latent process. The proposed approach was applied to traffic conflicts collected at the signal cycle level from four intersections in the city of Surrey, British Columbia. Traffic conflicts were measured by the modified time to collision (MTTC) indicator while traffic volume, shock wave area, average shock wave speed, and platoon ration of each cycle were employed as covariates. Four BHM models were developed, including a stationary model (i.e., BHM_GEV(0,0,0)) with no covariates and three non-stationary models (i.e., BHM_GEV(1,0,0), BHM_GEV(0,1,0), and BHM_GEV(1,1,0)) with covariates added to the location parameter, scale parameter, and both parameters of the GEV distribution, respectively. Traditional at-site GEV models were also developed for individual sites for comparison purposes. The results show that the BHM_GEV(1,1,0) is the best fitted model among the four models since considering covariates and unobserved heterogeneity significantly improves the model performance in terms of goodness of fit. The BHM_GEV(1,1,0) also yields relatively accurate and more precise crash estimates compared to the at-site models. This is attributed to the BHM_GEV(1,1,0) allowing borrowing strength from other sites. It is also found that the traffic volume, shock wave area, and platoon ratio have significant influence on the safety of signalized intersections. (C) 2019 Elsevier Ltd. All rights reserved.