There are two main issues associated with traffic conflict-based crash estimation. First, there are several conflict indicators which were shown to inherently represent partial severity aspects of traffic events. Therefore, combining more than one conflict indicator can result in more comprehensive understanding on the underlying level of safety. Second, the conflict extremes characterized by the indicators, which are most related to crashes, are rare and heterogeneous in nature. These issues need to be properly addressed to enhance the crash estimation from traffic conflicts. To this end, this study develops a bivariate Bayesian hierarchal extreme value modeling method, which consists of a bivariate extreme value model that integrates different conflict indicators in a unified framework and a Bayesian hierarchical structure that combines traffic conflicts of different sites and accounts for heterogeneity in conflict extremes. Two model estimation methods are proposed. The first is a two-stage method that estimates marginal distributions of individual conflict indicators (i.e., univariate Bayesian hierarchical extreme value model) at first and then estimates the dependence of the two indicators after marginal transformation. The second is a one-stage estimation that combines the transformation and dependence parameter inference in a single step to enable a potential gain in efficiency. The model estimation methods were applied to rear-end traffic conflicts collected at the signal cycle level from four intersections in the city of Surrey, British Columbia. The modified time to collision (MTTC) and post encroachment time (PET) were employed as conflict indicators. The traffic volume per cycle, shock wave area, and platoon ratio were considered as covariates to account for non-stationarity. The modeling results show that the standard errors of the model parameters of the bivariate Bayesian hierarchical extreme value model are smaller than those of the univariate Bayesian hierarchical extreme value models, which indicates more precise crash estimations of the bivariate model compared to univariate models. Meanwhile, the estimated crashes of the bivariate models also have a slightly higher accuracy. The more accurate and precise crash estimation is due to the bivariate model allowing the sharing of information from different conflict indicators.

与基于流量冲突的崩溃估计有两个主要问题。首先，有几种冲突指标被证明固有地代表了交通事件的部分严重性。因此，组合多个冲突指标可以导致对基本安全级别的更全面理解。第二，与崩溃最相关的指标所具有的极端冲突在本质上是罕见且异类的。这些问题需要适当解决，以增强因交通冲突而导致的崩溃估计。为此，本研究开发了一种双变量贝叶斯层级极值建模方法，它由一个将不同冲突指标整合到一个统一框架中的双变量极值模型和一个贝叶斯层次结构组成，该贝叶斯层次结构结合了不同站点的交通冲突并解释了冲突极端情况下的异质性。提出了两种模型估计方法。第一种是两阶段方法，首先评估单个冲突指标的边际分布（即，单变量贝叶斯分层极值模型），然后在边际变换后估算两个指标的依赖性。第二个是单阶段估计，将转换和相关性参数推断结合在一个步骤中，以实现潜在的效率提升。模型估计方法应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后端交通冲突。修改后的碰撞时间（MTTC）和侵占后时间（PET）被用作冲突指标。每个周期的交通量，冲击波面积和排比被视为协变量，以说明非平稳性。建模结果表明，双变量贝叶斯分层极值模型的模型参数标准误差小于单变量贝叶斯分层极值模型的模型误差，这表明与单变量模型相比，双变量模型的崩溃估计更精确。同时，估计的双变量模型崩溃也具有略高的准确性。