A likelihood ratio model for three-way data coupled with a PARAFAC model

Diesel fuel is often used as accelerant in arson due to its easy availability, cheapness, and easy induction of a fire. The investigation focuses on comparing the substance inside the canister found among the suspect belongings with the fire debris to find out if the fire could have been caused by the use of that particular diesel fuel. Finding an answer to the question if the compared samples, very likely weathered to different degrees, come from the same source, or not, requires considering the similarity and frequency of the data for both samples. It is, however, much more valuable when two samples with rare characteristics show similarity, because it is less likely. European Network of Forensic Science Institutes (ENFSI) is advocating the use of likelihood ratio (LR) then. The scope of the research was twofold: to find out if the LR models are capable of indicating that samples from the same source but weathered to different degrees are still so similar that they can be regarded as coming from a single source; to verify if the samples from different sources are easily identified as such regardless of their weathering state. The diesel samples weathered to different degrees were analysed using GC-MS. Hybrid LR models, which use just a few most significant and meaningful latent variables generated using chemometric tools, instead of many original characteristics, were proposed. PARAFAC (Parallel Factor Analysis) decomposition was applied and the ratios of the selected concentration mode loadings served as new variables for LR models. The research showed that there is a potential for discriminating between differently weathered samples using the LR framework, however the misleading evidence rates are still relatively high and the models need improvement. In 14% of comparisons between samples from different sources, the samples were found as coming from the same source, while in 8% of comparisons between differently weathered samples, but coming from the same source, the samples were found as originating from different sources.