Evaluation of glass samples for forensic purposes — An application of likelihood ratios and an information–theoretical approach

This article presents an experimental study about the influence of the selection of an adequate database for evidence evaluation using chemical profiles. Evidence evaluation in the forensic sense can be seen as the comparison of two glass objects, one of known origin, denoted as control glass, and typically would be from the scene of a crime, and the other one of unknown origin, termed recovered glass, which might be found in association with a suspect. The aim is to obtain some estimate of the weight of evidence for the degree of support to any of the hypothesis in the case, typically these might be that the control and recovered glass come from the same source (θp), and control and recovered glass come from different sources (θd). A likelihood ratio is considered a suitable measure of the evidential weight for the competing propositions. The observations are of the elemental composition of glass, measured using a Scanning Electron Microscopy, coupled with an Energy Dispersive X-ray spectrometer technique. A number of glass objects have been analyzed and their chemical profiles form a database which represents several sources of variation. In this paper questions surrounding the choice of observations to make are addressed empirically by assessing the impact of building each model using a database different from the one using for comparison. The performance of each evidence evaluation method is assessed by classical methods such as Tippett plots, or more recent information–theoretical approaches such as empirical cross-entropy (ECE) plots. The results show that several of the compositional elements are very robust to the selection of the background database, namely; calcium, silicon and sodium observed in their oxide forms. We also show that the likelihood ratio computed with the combination of these variables show a remarkable discriminating power, and good calibration, allowing them to be employed for the calculation of the strength of evidence in forensic case work.