Bayesian hybrid gamma-GPD model for extreme traffic conflict threshold determination in the peak over threshold approach

Extreme value theory (EVT) models have been frequently utilized to estimate crash risk from traffic conflicts with the peak over threshold commonly used to identify conflict extremes. However, a common problem for the peak over threshold method is the selection of a suitable threshold to distinguish general and extreme conflicts. Subjective and arbitrary selection of the threshold in peak over threshold method can result in bias and unstable estimation results. The primary objective of the study is to propose a hybrid modelling approach for the threshold determination in peak over threshold method. The hybrid model consists of a joint gamma distribution and generalized Pareto distribution (GPD). The gamma distribution is used to fit general conflicts while the GPD is used to fit extreme conflicts. Specially, discontinued, continued and differentiable gamma-GPD models are developed with the threshold being treated as a model parameter. Traffic conflict data collected from three signalized intersections in the city of Surrey, British Columbia were used for the study. The modified time to collision (MTTC) was employed as conflict indicator. The Bayesian approach was employed to estimate the threshold as well as other hybrid gamma-GPD model parameters. The results show that the discontinued gamma-GPD model is superior to the continued and differentiable gamma-GPD models for determining the threshold in terms of crash estimation accuracy and model fit. The crash estimates using the threshold determined by the hybrid gamma-GPD model outperform those estimated based on the traditional quantile plots method, indicating that the superiority of the proposed threshold determination approach based on gamma-GPD hybrid model. The proposed hybrid gamma-GPD model could determine the threshold parameter in peak over threshold method for traffic conflicts extremes automatically in an objective and quantitative way. It contributes to existing peak over threshold method for producing reliable crash estimation.