Forensic comparison of pyrograms using score-based likelihood ratios

The comparative analysis of chromatographic profiles of materials is the subject of interest in many scientific fields, including forensic science. Plastic microtraces collected during hit-and-run accidents and examined with pyrolysis gas chromatography mass spectrometry (Py-GC-MS), may serve as an example. The aim of comparing the recovered and control samples is to help reconstruct the event by commenting on their common, or not, sources. The objective is to report the evidential value of data in the context of two competing hypotheses: H1 - both samples share common origins (e.g. car) and H2 - they do not share common origins. The likelihood ratio approach (LR) addresses this idea as an acknowledged method within the forensic community. However, conventional feature-based LR models (using e.g. signal intensities of the chromatographically separated compounds) suffer from the curse of multidimensionality. Their considerable complexity can be reduced in the score-based LR models. In this concept the evidence expressed by the score, computed as a distance between the recovered and control samples characteristics, is evaluated using LR. A score solely based on a distance or a measure of similarity, without taking into account typicality, may not reflect the differences between similar samples clearly in a highly multidimensional space. Here we show that boosting the between-samples variance (B) whilst minimising the within-samples variance (W) helps distinguish between samples and improves the score-based LR models performance. Instead of computing the distances in the feature space, the authors use the space defined by ANOVA simultaneous component analysis, regularised MANOVA and ANOVA target projection that find directions with the magnified differences between B and W. The concept was successfully illustrated for 22 plastic containers and automotive samples, examined using Py-GC-MS. The research shows that this so-called hybrid approach combining chemometric tools and score-based LR framework yields a performing solution for the comparison problem for Py-GC-MS chromatograms.