Bayesian dynamic extreme value modeling for conflict-based real-time safety analysis

Real-time safety analysis and optimization using surrogate safety measures such as traffic conflicts and techniques such extreme value theory (EVT) models is an emerging research topic in the context of proactive traffic safety management. However, the predictive performance and temporal transferability of the existing real-time safety analysis EVT models are subject to the assumption of invariant model parameters, which do not account for the temporal variability and is not suitable for real-time traffic data analysis. This study proposes a Bayesian dynamic extreme value modeling approach for conflict-based real-time safety analysis which integrates a Bayesian dynamic linear model with the extreme value distribution. The proposed approach has several unique advantages as it: 1) allows the model parameters to be time-varying; 2) integrates the newer data with prior information to recursively update the model parameters and account for state-space changes and react to sudden trend changes; 3) accounts for temporal variability and non-stationarity in conflict extremes; and 4) quantitatively evaluates the real-time safety levels of a road facility. The proposed approach is applied for cycle-by-cycle safety analysis at four signalized intersections in the city of Surrey, British Columbia. Traffic conflicts are characterized by the modified time to collision indicator. Three traffic parameters (traffic volume, shock wave area, and platoon ratio) at the signal cycle level are considered as covariates to account for non-stationarity. Several Bayesian dynamic and static extreme value models are developed and two safety indices, namely risk of crash (RC) and return level (RL), are generated to quantitatively represent the cycle-level safety. The RC directly reflects whether a cycle is risky while the RL can evaluate the safety levels of individual cycles. The results show that the dynamic model can identify more crash-risk cycles with either a positive RC or a positive RL than the static model and is more capable of differentiating the safety levels for individual cycles in terms of RL. Overall, the dynamic model outperforms the static model in terms of the statistical fit and aggregate crash estimation accuracy.