Improving calibration of forensic glass comparisons by considering uncertainty in feature-based elemental data

Abstract The computation of likelihood ratios (LR) to measure the weight of forensic glass evidence with LA-ICP-MS data directly in the feature space without computing any kind of score as an intermediate step is a complex problem. A probabilistic two-level modeling of the within-source and between-source variability of the glass samples is needed in order to compare the elemental profiles measured from glass recovered from a suspect or a crime scene and compared to glass samples of a known source of origin. Calibration of the likelihood ratios generated using previously reported models is essential to the realistic reporting of the value of the glass evidence comparisons. We propose models that outperform previously proposed feature-based LR models, in particular by improving the calibration of the computed LRs. We assume that the within-source variability is heavy-tailed, in order to incorporate uncertainty when the available data is scarce, as it typically happens in forensic glass comparison. Moreover, we address the complexity of the between-source variability by the use of probabilistic machine learning algorithms, namely a variational autoencoder and a warped Gaussian mixture. Our results show that the overall performance of the likelihood ratios generated by our model is superior to classical approaches, and that this improvement is due to a dramatic improvement in the calibration despite some loss in discriminating power. Moreover, the robustness of the calibration of our proposal is remarkable.