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Supplementary File: Detection and Characterization of Ignitable Liquid Residues in Forensic Fire Debris Samples by Comprehensive Two-Dimensional Gas Chromatography

Forensic examination of fire debris is a notoriously difficult analytical task due to the complexity and variability of samples encountered. The development of increasingly sophisticated analytical instrumentation facilitates greater sensitivity while drastically increasing the abundance of data produced in a single analytical run. Hybrid methods combining chemometrics and forensic statistics have been developed in order to make optimal use of the complex analytical results. This dissertation addresses the interpretation of such measurements by considering competing hypotheses and using appropriate forensic reference data. Both detection and classification tasks for ignitable liquid residue in fire debris samples are explored as valuable contributions to the investigative process and potential use in a judicial context. Assessing the evidential value of the measurements requires understanding of the analytical signal in addition to extensive comprehension of the many sources of variation within and between samples. Preliminary data processing of chromatographic samples is explored including a discussion of both common practices and an exposition of novel techniques. The statistical modelling of chemically distinctive classes of ignitable liquids and the identification of their potentially discriminative characteristics is also presented. The methods and results presented herein emphasize the importance of a deep understanding of the data produced by analytical methods and a rigorous assessment of the statistical and computational assumptions made when articulating their evidential value. Statistical interpretation of fire debris analyses is based on a general probabilistic (likelihood ratio) framework for interpretation and evaluation of evidence.

In this thesis I consider the evaluation of a combination of different pieces of evidence in a legal and a forensic context. Evaluation of forensic evidence is the main topic of a research area called forensic statistics. In forensic statistics, the likelihood ratio framework is regarded as the standard for evaluating evidence. In legal practice, it is common that two competing propositions are presented to the trier of fact. The trier of fact needs to establish whether the proposition presented by the prosecution can be proven to the extent that there could be no ‘reasonable doubt’ in the mind of a ‘reasonable person’ that the defendant is guilty. The presented evidence should rule out any reasonable doubt. The likelihood ratio framework is based on probabilistic inference by applying Bayes’ Theorem. It allows for the transition from prior (initial) belief regarding the presented propositions to posterior (final) beliefs. This transition is based on the conditional probabilities to observe the evidence given the propositions (the likelihood ratio). In forensic casework, it is common that multiple pieces of evidence that need to be evaluated in terms of their support regarding the presented propositions are available. The most straightforward way of doing this for a forensic expert is by presenting a separate likelihood ratio for each individual piece of evidence. However, when doing so, one needs to be confident that the individual reports are optimally combined by the trier of fact. When forensic experts believe that their knowledge regarding the dependency structure between pieces of evidence is lost by presenting the likelihood ratios separately, one should strive to combine this evidence before it is sent to the trier of fact. Especially in situations where the pieces of evidence are of the same type (e.g. two shoe marks), one usually cannot regard them as conditionally independent observations and a combined evaluation is needed to prevent unnecessary misconceptions.