Score based procedures for the calculation of forensic likelihood ratios - Scores should take account of both similarity and typicality.

Score based procedures for the calculation of forensic likelihood ratios are popular across different branches of forensic science. They have two stages, first a function or model which takes measured features from known-source and questioned-source pairs as input and calculates scores as output, then a subsequent model which converts scores to likelihood ratios. We demonstrate that scores which are purely measures of similarity are not appropriate for calculating forensically interpretable likelihood ratios. In addition to taking account of similarity between the questioned-origin specimen and the known-origin sample, scores must also take account of the typicality of the questioned-origin specimen with respect to a sample of the relevant population specified by the defence hypothesis. We use Monte Carlo simulations to compare the output of three score based procedures with reference likelihood ratio values calculated directly from the fully specified Monte Carlo distributions. The three types of scores compared are: 1. non-anchored similarity-only scores; 2. non-anchored similarity and typicality scores; and 3. known-source anchored same-origin scores and questioned-source anchored different-origin scores. We also make a comparison with the performance of a procedure using a dichotomous "match"/"non-match" similarity score, and compare the performance of 1 and 2 on real data.