Constructing coherent score-based likelihood ratios that account for rarity

Score-based likelihood ratios (SLRs) are the most practical alternative to feature-based likelihood ratios for the evaluation of complex forensic evidence. The construction of effective general score functions, however, has received little attention. Many scores are measures of dissimilarity between two pieces of evidence. However, it is not always obvious which two pieces of evidence should be compared. This leads to applications of SLRs that suffer from incoherence, e.g. when you change the order in which the propositions are considered and the resulting SLR value is different from what is expected. We argue that this problem with SLRs should not be characterized as incoherence, but rather the comparison of two SLRs based on different score functions. Another common criticism of SLR approaches is that they do not account for the rarity of the features in a relevant background population. Towards this end, we build scores by aggregating many dissimilarity metrics and discuss potential relationships to rarity. Furthermore, we demonstrate that the resulting SLRs are both coherent and superior to standard scores via simulations.