### Bayesian reconstruction of traffic accidents

G. A. Davis
2003 Law, Probability and Risk
(Limit: 200 words) Traffic accident reconstruction has been defined as the effort to determine, from whatever evidence is available, how an accident happened. Traffic accident reconstruction can be treated as a problem in uncertain reasoning about a particular event, and developments in modeling uncertain reasoning for artificial intelligence can be applied to this problem. Physical principles can usually be used to develop a structural model of the accident and this model, together with an
more » ... ogether with an expert assessment of prior uncertainty regarding the accident's initial conditions, can be represented as a Bayesian network. Posterior probabilities for the accident's initial conditions, given evidence collected at the accident scene, can then be computed by updating the Bayesian network. Using a possible worlds semantics, truth conditions for counterfactual claims about the accident can be defined and used to rigorously implement a "but for" test of whether or not a speed limit violation could be considered a cause of an accident. The logic of this approach is illustrated for a simplified version of a vehicle/pedestrian accident, and then the approach is applied to determine the causal effect of speeding in 10 actual accidents. In Technical Report 1 for this project we argued that traffic accidents should be treated as resulting from the workings of partially understood, deterministic processes, and that the causal effect of some variable could, at least in principle, be determined "bottom up," by considering that variable's effect on each of a set of individual accidents. Since this requires that we reason in a logical manner about the uncertainty attached to particular events, we are faced with a problem more like determining an individual's cause of death, or identifying the perpetrator of a crime, than like estimating a summary measure for some population of entities. At the First International Conference on Forensic Statistics Lindley (1991) argued that the probability calculus should be applied not only to statistical problems, but to forensic inference more generally. Lindley focused on a class of problems for which the hypotheses of interest were the guilt or innocence of a defendant, and the task was to weigh the plausibility of these alternatives in the light of evidence. His proposed solution was Bayesian, where one first determines a prior assignment of probability to the alternative hypotheses, along with the probability of the evidence given each alternative, and then uses Bayes theorem to compute posterior probabilities for the hypotheses. This approach has since been applied to increasingly more complicated problems in forensic identification (e.g. Balding 2000; Dawid and Mortera 1998), in part due to an intense interest in interpreting DNA evidence.