Statistical Methods for Comparison of Forensic Glass Samples in Australia

Abstract

Glass is often broken when a crime is committed, whether it be a case of breaking and entering or a hit and run vehicle incident, for example. Forensic scientists may be tasked with analysing the broken glass in a number of ways. They may be asked to establish how the glass was broken, for example the type of instrument used to break the glass and whether it was broken from the inside or the outside. They may also be asked to connect a suspect with having been at the scene of the crime. In this thesis we restrict our focus to statistical methods to make comparison between two fragments of broken glass: one from the crime scene and another found on the clothing of a suspect. The chemical composition of the glass is measured by a technique known as laser ablation-inductively couple plasma mass spectrometry (LAICPMS). We show that machine learning methods, decision trees in particular, provide near-perfect prediction accuracy, improving on the currently employed methods. Further, the strength of evidence can be quantified by extending these methods and by constructing score-based likelihood ratios – a benefit otherwise only given by the traditional likelihood ratio methods. We find that these traditional likelihood ratio-based procedures do not offer an improvement in terms of prediction accuracy, and in fact perform worse than the current methodologies in this regard. These results demonstrate that a great deal of prediction accuracy can be gained by taking full advantage of the multivariate structure of the LAICPMS data. While glass evidence only constitutes a single component of a legal case, it is important that the methods used to evaluate the data are high in accuracy. In particular, in correspondence with the philosophy of “innocent until proven guilty”, our models perform well in minimising the rate at which samples are incorrectly classified as matching.