A multivariate extension to the standard 4σ criterion for comparison of forensic glass evidence

This manuscript presents a more accurate and easy to implement multivariate generalisation of the international standard 4σ forensic glass comparison technique. Many crimes result in glass breaking, and the broken glass found at a crime scene can be important forensic evidence. The chemical composition of this glass can be measured to establish whether it can be distinguished from glass fragments found on a suspect's clothing. The chemical composition can be measured using laser ablation-inductively coupled plasma mass spectrometry. A commonly used method to compare fragments of glass is the 4σ interval criterion. This method, however, compares each element individually and does not take advantage of the multivariate nature of this data. We introduce a multivariate extension to this method, which makes use of the correlation structure between the elements. We demonstrate that this method results in an improvement in the false positive rate, with only a small compromise in the false negative rate. The improvement in false positive rate is desirable as false positives translate to misleading evidence against a potentially innocent defendant. The multivariate generalisation improves accuracy while retaining a similar interpretation, and so is suitable to present in court.