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Bayesian hierarchical non-stationary hybrid modeling for threshold estimation in peak over threshold approach
Quansheng Yue1, Yanyong Guo1, Tarek Sayed2
1School of Transportation, Southeast University, Nanjing 211189, China; Jiangsu Key Laboratory of Urban ITS, Jiangsu Collaborative Innovation Center of Modern Urban Traffic Technologies, China.
Accident; Analysis and Prevention
|September 25, 2025
Summary
This study introduces an objective method for setting thresholds in traffic crash risk analysis, improving reliability over subjective approaches. The new Bayesian hierarchical modeling method enhances crash estimation accuracy.
Area of Science:
- Traffic safety and extreme value theory.
- Development of advanced statistical modeling for transportation research.
Background:
- The peak over threshold (POT) approach is crucial for crash risk estimation but suffers from subjective threshold selection, leading to biased results.
- Objective threshold determination is needed to improve the reliability of extreme value theory (EVT) applications in traffic safety.
Purpose of the Study:
- To develop and validate a hybrid modeling method for objective threshold determination in crash risk estimation.
- To compare five distinct non-stationary Bayesian hierarchical hybrid models (BHHM) and identify the optimal distribution for traffic conflicts.
- To enhance existing EVT methods for reliable crash estimations.
Main Methods:
- Developed a non-stationary framework where thresholds vary with real-time traffic covariates.
- Implemented Bayesian hierarchical structure to combine data from multiple sites, accounting for covariates and heterogeneity.
- Compared five non-stationary BHHM models (Normal-GPD, Cauchy-GPD, Logistic-GPD, Gamma-GPD, Lognormal-GPD) against traditional methods.
Main Results:
- The proposed BHHM approach objectively estimates the threshold parameter.
- Non-stationary BHHM models dynamically capture threshold variations across signal cycles based on traffic status.
- The Lognormal-GPD model demonstrated superior crash estimation accuracy and model fit compared to other BHHM models.
- BHHM-determined thresholds yielded more accurate crash estimates than graphical diagnostic and quantile regression approaches.
Conclusions:
- The hybrid modeling method provides an objective and reliable approach to threshold determination in crash risk analysis.
- The non-stationary BHHM framework enhances the accuracy and reliability of traffic safety estimations.
- This research offers a significant advancement in EVT applications for transportation safety, improving predictive capabilities.
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