Effects of sample size on pedestrian crash risk estimation from traffic conflicts using extreme value models

Sample size plays a critical role in an Extreme Value Theory (EVT) model for estimating crash risks from traffic conflicts. Many studies have raised concerns regarding sample size and its consequent negative impact on the performance of EVT models. However, the effects of sample size on EVT models are not well-known, requiring an extensive investigation and a deeper understanding of the effects of sample size on model performance. Motivated by this research gap, this study proposes a systematic approach to examine the effects of sample size on EVT models aimed at estimating pedestrian crash risks from traffic conflicts. Ten smaller and homogeneous samples of traffic conflicts are derived from a total of 144 h of video data collected from three signalised intersections in Brisbane, Australia, whereby vehicle–pedestrian conflicts are measured by post encroachment time. To ensure that each subset contains equal data from three intersections, samples are formed using a uniform distribution, and their effects are tested using non-stationary Block Maxima and Peak Over Threshold models estimated in the Bayesian framework. Results show that the sample size influences the prediction of mean crash frequencies, confidence intervals, and relative errors. Although the effect of sample size is non-uniform, the model performance appears to improve with the increase in sample size, whereby the block maxima models show higher sensitivity towards sample size variation, and the peak over threshold models reveal relatively stable and better performance. Moreover, a comparison of sample size thresholds indicates that the peak over threshold approach is more cost-efficient than its counterpart. Overall, the findings of this study demonstrate that improper sample size can lead to poor predictability, low reliability, and large uncertainties.