The role of isotope ratio mass spectrometry as a tool for the comparison of physical evidence

Abstract

This paper considers how likelihood ratios can be derived for a combination of physical, chemical and isotopic measurements. Likelihood ratios were formulated based on the characteristics of a small convenience sample of 20 duct tapes. The propositions considered were: Hp two samples are from the same batch Hd two samples are from different batches. The physical and isotopic characteristics of ten rolls of duct tape were shown to be consistent throughout each roll. The width and thickness of the tapes and the density of the scrim fibres provided equivalent information and the combined physical characteristics provided a basis upon which to discriminate between many of the samples. Scatter-plots and confidence ellipses provided a convenient method to group the isotopic composition of the tape backing material and provided a basis to discriminate between samples which were physically indistinguishable. Considering both the physical and isotopic characteristics it was possible, at best, to ascertain that the evidence provided moderately strong support for the proposition that two samples of tape were derived from the same batch (LR = 400). Kernel density estimates were used to model the distribution of isotopic compositions of the backing material. Using this technique it was possible to estimate objectively the probability that a sample with given characteristics could be drawn, at random, from the background population and to calculate a likelihood ratio based on the propositions above. The strength of evidence which could be presented by either model was ultimately limited by the size of the background sample.