Stochastic method based on copulas for predicting severe road traffic interactions

A major difficulty in assessing road traffic safety is the scarcity of historical accident data. xxThis is a common problem in contexts where a certain level of safety has been reached or where exposure is low, such as mixed traffic conditions with different levels of transport automation. Recent studies have demonstrated how severe interactions between road users and/or road users and infrastructure can be a direct measure of safety. However, limiting the investigation to only the most extreme events may lead to inconclusive results considering the lack of prediction robustness and the possible selection bias. In this context, extreme value theory (EVT) is commonly used to extrapolate crashes from road traffic interactions, even combining several indicators. The present work extends the EVT paradigm by proposing a method based on copula functions and EVT, which enables a more specific and continuous evaluation of interaction severity. Compared with pure EVT, this new approach extends the boundary to interactions of all severities while implicitly assuming that the relationship between safety-relevant events and road casualties is stochastic. This EVT-copula approach was also compared with bivariate peaks over threshold (BPOT). It was found that the two approaches yield similar prediction results for crash probabilities. Furthermore, the proposed approach applies to events not properly defined in BPOT and provides more accurate predictions for severe (and less severe) interactions compared with BPOT, when benchmarked against observations.