A bivariate Bayesian hierarchical extreme value model for traffic conflict-based crash estimation

Abstract 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.

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