A bayesian approach to cross-validation in pedestrian accident reconstruction

In statistical modeling, cross-validation refers to the practice of fitting a model with part of the available data, and then using predictions of the unused data to test and improve the fitted model. In accident reconstruction, cross-validation is possible when two different measurements can be used to estimate the same accident feature, such as when measured skidmark length and pedestrian throw distance each provide an estimate of impact speed. In this case a Bayesian cross-validation can be carried out by (1) using one measurement and Bayes theorem to compute a posterior distribution for the impact speed, (2) using this posterior distribution to compute a predictive distribution for the second measurement, and then (3) comparing the actual second measurement to this predictive distribution. An actual measurement falling in an extreme tail of the predictive distribution suggests a weakness in the assumptions governing the reconstruction. This paper describes an implementation of these ideas using the Bayesian freeware WinBUGS. A statistical version of a throw distance model was fitted to data from 55 staged collisions between adult pedestrian dummies and sedan-type vehicles, while a standard braking-to-stop model was used to relate skidmark length to vehicle speed. Cross-validation is then illustrated using an additional 15 staged collisions. In 13 of the 15 cases the skidding and throw models yielded consistent results, while in two cases the resulting impact speed estimates were substantially different. In both of the discrepant cases it was possible to identify the sources of the discrepancies, and produce consistency once these were accounted for.