Network-wide multi-horizon probabilistic crash risk forecasting: A Bayesian hierarchical marked point process model with spatial dependence

Forecasting crash risk at the network level over future horizons is fundamental to proactive safety management. Existing conflict-based extreme value theory (EVT) models, however, largely ignore spatial correlations in extreme traffic conflicts and remain restricted to one-step-ahead crash risk forecasts. This study addresses both limitations by proposing a score-driven peak-over-threshold (SPOT) model within a marked point process framework, combined with conditional autoregressive spatial priors in a Bayesian hierarchical structure to account for spatial dependence across the network. Probabilistic forecasts of two crash risk measures, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), are generated at multiple future horizons via posterior simulation of the marked point process. The framework is applied to an urban network of 50 intersections from the pNEUMA drone trajectory dataset in Athens, Greece. In-sample results reveal meaningful spatial correlation, and model comparison shows that covariate specification has a substantially larger impact on predictive performance than spatial prior choice. Out-of-sample, crash risk forecasts are most reliable within 20 s. Forecast quality degrades at longer horizons due to growing simulation errors and parameter reversion toward baseline levels, becoming inadequate beyond 60 s. The practical value of the framework is demonstrated through a forecast-based safest-route finding application, which yields routes that are on average 7% safer than those based on static crash risk estimates with comparable travel times.