This study presents a Bayesian hierarchical model to estimate crashes from traffic conflict extremes in a non-stationary context. The model combines a peak over threshold approach with non-stationary thresholds in terms of regression quantiles and covariate-dependent parameters of the generalized Pareto distribution. The developed model was applied to estimate rear-end crashes from traffic conflicts of the same type collected from four signalized intersections. The conflicts were measured by the modified time to collision (MTTC) and traffic volume, shock wave area, average shock wave speed, and platoon ratio of each signal cycle were employed as covariates. Thresholds corresponding to quantiles ranging from 80% to 95% were tested and the threshold stability plot indicated the 90% quantile was reasonable. Threshold excesses were then declustered at the signal cycle level, and the remained ones were used to develop the Bayesian hierarchical generalized Pareto distribution models (BHM_GPD). The model estimation results show that accounting for non-stationarity significantly improves the model fit. As well, the best fitted model generated accurate crash estimates with relatively narrow confidence intervals. The developed BHM_GPD model was also compared to the Bayesian hierarchical generalized extreme value model (BHM_GEV). The results show that the two models generate comparable crash estimates in terms of accuracy, but the crash estimates from the BHM_GPD model are generally more precise than those of BHM_GEV model. It is also found that although the peak over threshold approach combined with declustering reduces the number of extreme samples, it ensures the use of actual extremes. Moreover, the limited sample size issue is overcome by the proposed Bayesian hierarchical framework, which allows sharing information from different sites and accounting for unobserved heterogeneity. The findings also imply that the BHM_GEV model is preferred when traffic conflicts are relatively evenly distributed over blocks; otherwise the BHM_GPD model should be a better choice.

这项研究提出了一种贝叶斯分层模型，用于估计非平稳情况下交通冲突极端事件造成的崩溃。该模型在回归分位数和广义Pareto分布的协变量相关参数方面结合了峰值超过阈值方法和非平稳阈值。所开发的模型用于估计从四个信号交叉口收集的同一类型的交通冲突引起的追尾事故。通过修改的碰撞时间（MTTC）来衡量冲突，并使用交通量，冲击波面积，平均冲击波速度和每个信号周期的排比作为协变量。测试了与80％到95％范围内的分位数相对应的阈值，并且阈值稳定性图表明90％的分位数是合理的。然后在信号周期级别上对阈值过高进行聚类，然后将剩余的阈值过高用于开发贝叶斯分层广义Pareto分布模型（BHM_GPD）。模型估计结果表明，考虑非平稳性可显着提高模型拟合度。同样，最佳拟合模型以相对窄的置信区间生成了准确的碰撞估计。还将开发的BHM_GPD模型与贝叶斯分层广义极值模型（BHM_GEV）进行比较。结果表明，这两个模型在准确性方面产生了可比的崩溃估计，但是BHM_GPD模型的崩溃估计通常比BHM_GEV模型的崩溃估计更精确。还发现，虽然“超阈值方法”与“去聚类”相结合会减少极端采样的数量，它确保使用实际的极端情况。此外，提出的贝叶斯分级框架克服了样本量有限的问题，该框架允许共享来自不同站点的信息并考虑到未观察到的异质性。研究结果还暗示，当交通冲突相对均匀地分布在区块上时，BHM_GEV模型是首选模型；否则，BHM_GPD模型应该是一个更好的选择。