Dynamic Bayesian hierarchical peak over threshold modeling for real-time crash-risk estimation from conflict extremes

Using traffic conflict-based extreme value theory (EVT) models to quantify real-time crash-risk of road facilities is a promising direction for developing proactive traffic safety management strategies. Existing EVT real-time crash-risk analysis studies have only focused on using block maxima models. This study proposes a dynamic Bayesian hierarchical peak over threshold modeling approach to estimate real-time crash-risk based on traffic conflicts. The proposed approach combines quantile regression, dynamic updating approach, Bayesian hierarchical structure, and the peak over threshold method to generate time-varying generalized Pareto distributions to derive real-time crash-risk measures (i.e., crash probability and return level). The derived real-time crash-risk measures are applied to estimate cycle-level crash-risk at three signalized intersections in Surrey, British Columbia. Five approaches are used to dynamically update the model parameters, including time trend model, generalized autoregressive conditional heteroskedasticity process approach, as well as the first-order, second-order, and third-order dynamic linear models. For comparison, static models are also developed. All the developed models are compared in terms of statistical fit and predictive performance. Based on the best fitted dynamic model, cycle-level crash probability and return level are calculated to measure signalized intersection safety at cycle level. The results show that dynamic models considerably outperform static models in terms of statistical fit and predictive performance. Further, the third-order dynamic model has the best performance, which is probably due to that the model incorporates two linear trends to respectively describe the variation of the coefficients as well as its change to better account for the variation in the effect of time-varying covariates. However, it should be noted that the third-order dynamic model development needs more computation time than other dynamic models, which may limit the application of the model.