Combining multiple pieces of evidence using a lower bound for the LR

Abstract

In forensic casework it is common that multiple pieces of evidence are obtained in a single case. For the evaluation of such evidence, one cannot simply assume that they originated from the same source. If this can be disputed, one could decide to report the evidential value of the separate pieces by computing likelihood ratios (LRs) for them separately. However, by doing so, information regarding the conditional dependency structure is lost and the potentially difficult step of combining them is left to the trier of fact. Especially in situations where the pieces of evidence are of the same type, a combined evaluation could be substantially more informative. In such situations, it is not unrealistic that the separate evidential values are not optimally combined by the trier of fact. From a scientific point of view, the optimal way is that the forensic scientist combines the forensic evidence in a report using hypotheses at the 'activity level'. In practice, however, this is not always feasible for every case for reasons of efficiency. In this article, we explore what can be done in cases where the optimal solution is too costly. For a combined evaluation, the prior distribution for the number of distinct sources of the pieces of evidence becomes part of the LR. Generally, prior probabilities are beyond the scope of expertise of the forensic specialist and are left to the trier of fact to decide.Wepropose a lower bound LRapproach for such situations that is independent of the prior distribution. Using a set of examples, we present how this method can be applied in practice.