Extreme value theory (EVT) has been utilized to estimate crash risk from traffic conflicts with the peak over threshold approach. However, it's challenging to determine a suitable threshold to distinguish extreme conflicts in an objective way. The subjective and arbitrary selection of the threshold in the peak over threshold approach can result in biased estimation outcomes. This study proposes a Bayesian hierarchical hybrid modeling (BHHM) framework for the threshold estimation in the peak over threshold approach. Specifically, BHHM is based on a piecewise function to model the general conflicts with specific distribution while model the extreme conflicts with generalized Pareto distribution (GPD). The Bayesian hierarchical structure is used to combine traffic conflicts from different sites, incorporating covariates and site-specific unobserved heterogeneity. Five non-stationary BHHM models, including Normal-GPD, Cauchy-GPD, Logistic-GPD, Gamma-GPD, and Lognormal-GPD models, were developed and compared. Traditional graphical diagnostic and quantile regression approaches were also used for comparison. Traffic conflicts collected from three signalized intersections in the city of Surrey, British Columbia were used for the study. The results show that the proposed BHHM approach could estimate the threshold parameter objectively. The Lognormal-GPD model is superior to the other four BHHM models in terms of crash estimation accuracy and model fit. The crash estimates using the threshold determined by the BHHM outperform those estimated based on the graphical diagnostic and quantile regression approaches, indicating the superiority of the proposed threshold determination approach. The findings of this study contribute to enhancing the existing EVT methods for providing a threshold determination approach as well as producing reliable crash estimations.

翻译：极值理论已被应用于通过超越阈值法从交通冲突中估计事故风险。然而，如何客观地确定一个合适的阈值以区分极端冲突具有挑战性。超越阈值法中主观且随意的阈值选择可能导致有偏的估计结果。本研究提出了一个贝叶斯层次混合建模框架，用于超越阈值法中的阈值估计。具体而言，BHHM 基于分段函数，用特定分布对一般冲突进行建模，同时用广义帕累托分布对极端冲突进行建模。贝叶斯层次结构用于整合来自不同地点的交通冲突，并纳入协变量和地点特定的未观测异质性。研究开发并比较了五种非平稳 BHHM 模型，包括 Normal-GPD、Cauchy-GPD、Logistic-GPD、Gamma-GPD 和 Lognormal-GPD 模型。同时使用了传统的图形诊断法和分位数回归法进行比较。研究使用了从加拿大不列颠哥伦比亚省萨里市三个信号控制交叉口收集的交通冲突数据。结果表明，所提出的 BHHM 方法能够客观地估计阈值参数。在事故估计精度和模型拟合度方面，Lognormal-GPD 模型优于其他四种 BHHM 模型。使用 BHHM 确定的阈值进行的事故估计，其效果优于基于图形诊断法和分位数回归法得到的估计，这表明了所提出的阈值确定方法的优越性。本研究的结果有助于增强现有的极值理论方法，为其提供一种阈值确定方法，并产生可靠的事故估计。