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Technical Paper

Bayesian Uncertainty Quantification for Planar Impact Crashes via Markov Chain Monte Carlo Simulation

A continuing topic of interest is how to best use information from Event Data Recorders (EDR) to reconstruct crashes. If one has a model which can predict EDR data from values of the target variables of interest, such as vehicle speeds at impact, then in principle one can invert this model to estimate the target values from EDR measurements. In practice though this can require solving a system of nonlinear equations and a reasonably flexible method for carrying this out involves replacing the inverse problem with nonlinear least-squares (NLS) minimization. NLS has been successfully applied to two-vehicle planar impact crashes in order to estimate impact speeds from different combinations of EDR, crush, and exit angle measurements, but an open question is how to assess the uncertainty associated with these estimates. This paper describes how Markov Chain Monte Carlo (MCMC) simulation can be used to quantify uncertainty in planar impact crashes.
Journal Article

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.