Analysis of lead isotopic ratios of glass objects with the aim of comparing them for forensic purposes

This paper presents the possibilities of applying the likelihood ratio (LR) approach for the comparison problem to the data collected as a result of the Isotope Ratio Mass Spectrometry (IRMS) analysis targeted at lead (Pb)-isotope ratios. The assessment of the applied LR models performance was conducted by an Empirical Cross Entropy (ECE) approach. 35 glass samples were subjected to IRMS analysis and were described by Pb-isotope ratios: 208Pb/204Pb, 207Pb/204Pb, 206Pb/204Pb, 208Pb/206Pb, and 207Pb/206Pb. Univariate and bivariate LR computations were performed, assuming normally distributed data subjected or not to a logarithmic transformation. Principal Component Analysis (PCA) was employed for creating orthogonal variables to propose an alternative LR model. It was found that the application of variable 208Pb/204Pb seems to be promising as it delivers one of the lowest percentages of false positive and false negative rates as well as being the only variable for which an ECE plot gave satisfactory results.