Multivariate Bayesian hierarchical modeling of the non-stationary traffic conflict extremes for crash estimation

Recent studies have developed univariate and bivariate Bayesian hierarchical extreme value models to improve traffic conflict-based crash estimation through addressing the issues of non-stationarity of conflict extremes and individual conflict indicators representing only partial severity aspects of a traffic event. Although the use of bivariate models showed considerable improvements compared to univariate models, two traffic conflict indicators may not be sufficient to cover all severity aspects of a traffic event. Therefore, a high dimensional multivariate Bayesian hierarchical extreme value model based on more than two conflict indicators merits further research. This study develops a multivariate Bayesian hierarchical extreme value modeling approach, which comprises a multivariate extreme value model and a Bayesian hierarchical structure. The former integrates several traffic conflict indicators in a unified framework, while the latter combines traffic conflicts from different sites, incorporating several covariates and site-specific unobserved heterogeneity. A model estimation approach for the multivariate Bayesian hierarchical extreme value model is proposed and applied to estimate rear-end crashes from four signalized intersections in the city of Surrey, British Columbia. The modified time to collision (MTTC), post encroachment time (PET), and deceleration rate to avoid a crash (DRAC) were employed as conflict indicators. Three covariates including traffic volume, shock wave area, and platoon ratio were considered to account for non-stationarity in conflict extremes. The results show that in terms of crash estimation accuracy, the high dimensional multivariate (e.g., trivariate) Bayesian hierarchical extreme value model outperforms both the low dimensional multivariate (e.g., bivariate) and univariate Bayesian hierarchical extreme value models. This is likely due to the multivariate model having the capability of sharing information across several different conflict indicators. (C) 2020 Elsevier Ltd. All rights reserved.