A cross-comparison of different extreme value modeling techniques for traffic conflict-based crash risk estimation

Extreme Value Theory (EVT) models have recently gained increasing popularity for crash risk estimation using traffic conflict data. Extreme value modeling consists of two fundamental approaches: the block maxima approach and the peak-over-threshold approach, each with several variants. However, a comprehensive comparison of these two approaches and their variants in crash risk estimation is lacking. This study bridges this gap by comparing different extreme value modeling techniques and evaluating their performance in estimating crash frequencies. Within a non-stationary Bayesian hierarchical modeling framework, the analyzed models include the block maxima model, the $r$ largest order statistic model, and the peak-over-threshold model with the fixed and dynamic threshold, across univariate and bivariate traffic conflict cases. The analysis utilizes modified time-to-collision and post-encroachment time conflict indicator data collected from four signalized intersections in the City of Surrey, British Columbia, Canada. The results show that incorporating additional order statistics in the $r$ largest order statistic model improves predictive performance, particularly with limited extreme conflict samples. Moreover, employing the dynamic threshold within the peak-over-threshold model enhances model goodness-of-fit and yields more accurate crash frequency estimates compared to using the fixed threshold. While the performance of the block maxima and peak-over-threshold models varies with the selected conflict indicator in the univariate case, the bivariate peak-over-threshold model with the dynamic threshold exhibits superior overall prediction accuracy over the corresponding block maxima model. This is likely due to the effectiveness of the dynamic threshold in precisely identifying truly critical extreme conflicts.