Evaluation of infrared spectra analyses using a likelihood ratio approach: A practical example of spray paint examination

Abstract

Depending on the forensic disciplines and on the analytical techniques used, Bayesian methods of evaluation have been applied both as a two-step approach (first comparison, then evaluation) and as a continuous approach (comparison and evaluation in one step). However in order to use the continuous approach, the measurements have to be reliably summarized as a numerical value linked to the property of interest, which occurrence can be determined (e.g., refractive index measurement of glass samples).For paint traces analyzed by Fourier transform infrared spectroscopy (FTIR) however, the statistical comparison of the spectra is generally done by a similarity measure (e.g., Pearson correlation, Euclidean distance). Although useful, these measures cannot be directly associated to frequencies of occurrence of the chemical composition (binders, extenders, pigments). The continuous approach as described above is not possible, and a two-step evaluation, 1) comparison of the spectra and 2) evaluation of the results, is therefore the common practice reported in most of the laboratories. Derived from a practical question that arose during casework, a way of integrating the similarity measure between spectra into a continuous likelihood ratio formula was explored. This article proposes the use of a likelihood ratio approach with the similarity measure of infrared spectra of spray paints based on distributions of sub-populations given by the color and composition of spray paint cans. Taking into account not only the rarity of paint composition, but also the “quality” of the analytical match provides a more balanced evaluation given source or activity level propositions. We will demonstrate also that a joint statistical–expertal methodology allows for a more transparent evaluation of the results and makes a better use of current knowledge.