A Bayesian deep learning-driven framework integrating non-stationary generalized extreme value parameterization for coneflict-based real-time crash risk prediction

Estimating crash risks by assessing traffic conflicts is in important advance in traffic safety and a significant departure from the traditional approach of waiting for crashes to occur to identify problematic highway segments and intersections. This has led to the development of various non-stationary (using time-varying covariates) Extreme Value Theory (EVT) approaches where traffic conflict data are used to estimate crash risks. However, many of these EVT applications have been limited by fixed functional relationships, reliance on prior assumptions, limited sets of covariates, and the inability to capture temporal dependencies among covariates. To overcome these limitations, this study proposes a Bayesian Deep Learning - Generalized Extreme Value (BDL-GEV) framework for real-time crash risk prediction. In this approach, a Long Short-Term Memory (LSTM)-based architecture is used to dynamically generate GEV distribution parameters from historical traffic states using tailored mapping functions to better quantify crash risks. In addition, to account for unobserved heterogeneity and predictive uncertainty, a random generator is embedded in the input layer, and a Bayesian deep learning formulation with a Monte Carlo dropout is used to provide principled, data-driven uncertainty quantification. Using rear-end traffic conflict data from a signalized intersection shows that the proposed framework produces stable and plausible GEV parameter estimates with appropriate uncertainty quantification. Negative log-likelihood value and Probability Integral Transform (PIT)-based diagnostics indicate that the model achieves a good distributional fit, and sensitivity analyses confirm the efficacy of the Bayesian component, random generator, parameter mapping strategy, sliding-window length and penalty term in the loss function. Finally, compared to the traditional Bayesian hierarchical GEV model, the proposed BDL-GEV model improves both distributional fitting and one-signal-cycle-ahead crash risk estimation.