Likelihood ratio methods for forensic comparison of evaporated gasoline residues

In the investigation of arson, evidence connecting a suspect to the fire scene may be obtained by comparing the composition of ignitable liquid residues found at the crime scene to ignitable liquids found in possession of the suspect. Interpreting the result of such a comparison is hampered by processes at the crime scene that result in evaporation, matrix interference, and microbial degradation of the ignitable liquid. Most commonly, gasoline is used as a fire accelerant in arson. In the current scientific literature on gasoline comparison, classification studies are reported for unevaporated and evaporated gasoline residues. In these studies the goal is to discriminate between samples of several sources of gasoline, based on a chemical analysis. While in classification studies the focus is on discrimination of gasolines, for forensic purposes a likelihood ratio approach is more relevant. In this work, a first step is made towards the ultimate goal of obtaining numerical values for the strength of evidence for the inference of identity of source in gasoline comparisons. Three likelihood ratio methods are presented for the comparison of evaporated gasoline residues (up to 75% weight loss under laboratory conditions). Two methods based on distance functions and one multivariate method were developed. The performance of the three methods is characterized by rates of misleading evidence, an analysis of the calibration and an information theoretical analysis. The three methods show strong improvement of discrimination as compared with a completely uninformative method. The two distance functions perform better than the multivariate method, in terms of discrimination and rates of misleading evidence.