How long is long enough for traffic conflict observation: An investigation using extreme value theory approaches

Determining the appropriate duration for traffic conflict observation remains a critical yet unresolved challenge in road safety analysis. Existing approaches lack a quantitative approach to determine adequate sample sizes for general conflict-based applications. This study addresses this gap by proposing an extreme value theory based framework to determine appropriate observation durations, based on the inherent stability of road entity safety for a specified period. Using approximately 50 hours of high-resolution LiDAR data from a signalized intersection in Harbin, China, conventional generalized Pareto distribution (GPD) models and Bayesian hierarchical GPD (BH_GPD) models were developed, considering variations in conflict types, intersection approaches, and sample sizes. Two safety indicators, the expected annual number of crashes and the crash return level, both derived from the GPD distribution, were employed to assess sample adequacy based on their respective rates of convergence. Results show that the crash return level, unlike traditional crash frequency metrics, remains non-zero and sensitive to observation duration even in low-risk scenarios, facilitating a more robust identification of adequate sample sizes. Notably, the BH_GPD model generally reduced required observation durations compared to standalone GPD models, particularly for low-conflict scenarios (i.e., less than 10 conflicts/hour), while yielding narrower credible intervals due to its ability to pool data across sites. A key finding reveals that adequate sample sizes range from 15 to over 45 hours for different scenarios, inversely correlated with conflict rates. This study establishes a quantitative framework to determine the adequate sample size of traffic conflicts, which has the potential to contribute significantly to the standardization of traffic conflict techniques in road safety research.