Bayesian forecasting of short-term crash risk with conditional extreme value models: A comparison between one-stage and two-stage approaches

• One-stage and two-stage conditional extreme value models are developed for crash risk forecasting in a Bayesian framework. • This study presents the first application of the GARCH-EVT model and its covariate-augmented variant in traffic safety. • Conditional Value-at-Risk (CVaR) is introduced as a new complementary crash risk measure. • A two-stage backtesting framework is applied to validate crash risk measure forecasts and compare model performance. • Both the score-driven peak-over-threshold and GARCH-EVT model yield valid short-term crash risk forecasts. Extreme Value Theory (EVT) has become a widely used approach for quantifying crash risk from traffic conflict data. Most existing applications, however, rely on unconditional models, which fail to adequately capture dependence in extreme traffic conflicts and do not reliably predict future crash risk. To demonstrate the potential of conditional EVT models for advancing short-term crash risk forecasting, this study compares two conditional EVT approaches within a Bayesian framework that address extremal dependence from distinct perspectives. The first approach is the two-stage GARCH-EVT framework, where conditional mean and variance are modeled using GARCH-type specifications before EVT is applied to the standardized residuals. Both traditional and covariate-augmented variants are examined. The second approach uses a one-stage conditional peak-over-threshold (POT) model, represented by the score-driven POT model, which directly captures dynamics in the conditional exceedance probability and the distribution of exceedance sizes. Crash risk is quantified using two conditional tail risk measures, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), with forecasting performance evaluated through traditional and comparative backtesting. An empirical study examines rear-end conflicts collected at two signalized intersections over four observation days to generate one-cycle-ahead crash risk forecasts during the out-of-sample period. Traditional backtesting indicates that both the covariate-augmented GARCH-EVT and the score-driven POT approaches produce valid and comparable forecasts, with the two-stage method yielding estimates with lower uncertainty. Comparative backtesting, however, shows that the score-driven POT model achieves slightly superior forecasting accuracy. The weaker performance of the two-stage framework can be attributed to partial removal of extremal dependence, sensitivity to substitute values in cycles without conflicts, and the limitations inherent in its two-stage structure.