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.