A Bayesian hierarchical spatio-temporal generalized extreme value modeling for safety analysis from traffic conflicts

Traffic conflicts at urban intersections often exhibit complex spatio-temporal correlations due to network topology and traffic flow dynamics. Ignoring these dependencies can lead to biased risk estimation and ineffective safety management. While Extreme Value Theory (EVT) is a state-of-the-art approach for proactive safety analysis, existing EVT models often overlook these critical spatial and combined spatio-temporal effects. To address this, this study develops a comprehensive Bayesian hierarchical spatio-temporal Generalized Extreme Value (GEV) modeling approach for non-stationary extreme traffic conflicts. A suite of GEV models, including spatial, temporal, and joint spatio-temporal variations, is proposed. The model integrates spatial correlation via conditional autoregressive structure and temporal correlation using a first-order random walk structure. The approach includes the development of two quantitative safety indices: the risk of crash and the return level, critical for dynamic risk assessment and management. Traffic conflict data from 16 urban intersections in Athens were used for empirical analysis. Results show that models incorporating spatial, temporal, or joint spatio-temporal effects significantly outperform the baseline model, reducing the Deviance Information Criterion (DIC) by averages of 238, 138, and 339, respectively. Crucially, the spatio-temporal GEV models provide the best overall fit, underscoring the necessity of jointly accounting for spatial and temporal effects. Finally, validation of the best-fitted model confirms its strong predictive accuracy, with an average difference of only 1.97 between estimated and observed extreme conflict counts, and the estimates consistently falling within the 95% confidence intervals of the observed risky events, thereby supporting its application for robust and dynamic safety management.