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.

贝叶斯分层建模（BHM）方法用于对不同站点的非平稳交通冲突极端进行建模，以进行崩溃估计。分层结构包括三层：使用通用极值（GEV）分布建模的数据层，将GEV的参数与协变量和未观察到的异质性相关的潜在高斯过程层，以及具有先前分布以表征特征的前一层。潜在过程。所提出的方法适用于从不列颠哥伦比亚省萨里市的四个路口以信号周期水平收集的交通冲突。通过修改的碰撞时间（MTTC）指标来衡量交通冲突，同时使用交通量，冲击波面积，平均冲击波速度和每个周期的排量作为协变量。开发了四个BHM模型，包括没有协变量的固定模型（即BHM_GEV（0,0,0））和三个非平稳模型（即BHM_GEV（1,0,0），BHM_GEV（0,1,0 ）和BHM_GEV（1,1,0）），并分别向GEV分布的位置参数，比例参数和两个参数中添加协变量。还为各个站点开发了传统的站点GEV模型，以进行比较。结果表明，BHM_GEV（1,1,0）是四个模型中的最佳拟合模型，因为考虑协变量和未观察到的异质性在拟合优度方面显着提高了模型性能。与现场模型相比，BHM_GEV（1,1,0）还可以得出相对准确，更精确的碰撞估计。这归因于BHM_GEV（1,1,0），它允许从其他站点借力。