Short-term conflict-based crash risk forecasting: A Bayesian conditional peak-over-threshold approach

Abstract

• Conditional peak-over-threshold models are introduced, with Bayesian inference for real-time crash risk forecasting. • Self-exciting and score-driven conditional peak-over-threshold specifications are demonstrated. • Score-driven peak-over-threshold models with Burr hazard function achieve superior crash risk forecasting performance. • Classical peak-over-threshold models underestimate crash risk by ignoring temporal dependence in extreme traffic conflicts. • The models enable uncertainty quantification in crash risk forecasting, supporting proactive safety interventions. Forecasting short-term crash risks is crucial for real-time road safety management, yet this research area remains largely underexplored. Classical Extreme Value Theory (EVT) models assume independent observations, limiting their ability to capture the clustering behavior in occurrence times and magnitudes of extreme traffic conflicts. To overcome this limitation, we introduce conditional peak-over-threshold (POT) models that incorporate time-varying parameters to simultaneously capture the dynamics of extreme traffic conflicts and enable forecasting for crash risk. Within the framework of marked point process (MPP) and EVT, we develop the conditional POT models based on two observation-driven approaches (self-exciting and score-driven) through Bayesian inference. A dynamic risk measure, Value-at-Risk (VaR), is employed to assess the performance of these conditional POT models for crash risk forecasting. Empirical analysis of rear-end conflict data collected from a signalized intersection across two separate days demonstrates that both self-exciting and score-driven POT models effectively characterize the clustering behavior of extreme traffic conflicts. Furthermore, backtesting confirms that conditional POT models provide more accurate crash risk forecasts than classical POT models, which tend to underestimate crash risk by ignoring temporal dependence in extreme traffic conflicts. Among the examined model specifications, score-driven POT models demonstrate superior forecasting performance. Our proposed Bayesian conditional POT approach provides probabilistic forecasting that enables direct uncertainty quantification and dynamic monitoring of crash risk, thereby supporting informed safety decisions.