# Machine Learning Subjective Opinions: An Application in Forensic Chemistry
## 2 Background  
### Fire Debris Analysis  
Fire debris analysis is an important and challenging area in forensic science. The main goal of fire debris analysis is to identify the presence or absence of an ignitable liquid residue (ILR) in samples collected from a fire scene. The analysis is typically carried out following the current ASTM E1618-19 protocol [12]. The analyst uses target compounds identified by GC-MS, extracted ion profiles (EIP), and chromatographic patterns to identify the presence of ILR in a sample. Some classes of ignitable liquid, as defined in the ASTM E1618-19 standard, have a characteristic chromatographic pattern, which can move throughout the chromatogram depending on the range of molecular weights (i.e., heavy, medium or light). Some classes are defined by components (i.e., those containing a significant oxygenated component, normal alkanes, aromatics, naphthalene-parafinic and isoparaffinics), some are product specific (i.e., gasoline), while processing defines the petroleum distillate class, and the miscellaneous class corresponds to mixtures of liquids from several classes, single components, and any ignitable liquid (IL) not belonging to another defined class.  
Figure 1: **(a)** Subjective opinion triangle with the three vertices labeled corresponding to the belief, disbelief and uncertainty components of an opinion. The types of opinions are shown as open symbols with an associated name and connecting line. **(b)** The subjective triangle showing a single, partially uncertain opinion of source A regarding the classification of a sample as belonging to state \(x\). The belief, disbelief and uncertainty values of source A regarding membership in class \(x\) (\(b_{x}^{A}\), \(d_{x}^{A}\), \(u_{x}^{A}\)) are shown in gray arrows. The dashed arrow going from the u-vertex to the value of the base rate (\(a_{x}^{A}\)) is the director line. The partially uncertain opinion is projected along a projector line parallel to the director line to a point on the base of the triangle corresponding to the expectation value of the opinion \(P(\omega_{x}^{A})\), see text.  
The ASTM E1618-19 reporting protocol requires an opinion expressed as a categorical statement regarding whether the sample contains ILR or not. Reporting in categorical statements corresponds to the analyst either reporting a \"decision\" or expressing an \"absolute opinion\", see Figure 1 and Section 2.5. In the terminology of subjective opinions, an \"absolute opinion\" implies total belief or disbelief and no accompanying uncertainty. The absence of uncertainty does not reflect the reality of the analysis of complex fire debris samples. A positive determination is based on the identification of ILR belonging to a defined class [12]. Partial evaporation (i.e., weathering) of the IL during the fire and possible biological degradation after the fire can complicate the identification of ILR patterns. In addition, pyrolysis of building materials and furnishings under the high temperatures of the fire produces interfering background chemical components that can mask the presence of ILR. In summary, fire debris analysis is a complicated pattern recognition process that under current practice is entirely based on the interpretation of the analyst, is subjective, and prone to bias. Fire debris analysis is a task that could potentially benefit from ML classification. The reporting protocol given in the ASTM E1618-19 standard does not use a statistical metric to describe the strength of the evidence and does not promote the use of ML methods to assist the analyst [12]. In a 2009 report, the National Academy of Sciences (NAS) recommended using language in reports and testimony that conveys proper confidence or significance [13]. The European Network of Forensic Science Institutes (ENFSI) embraces evaluative reporting, which emphasizes the likelihood ratio as a measure of the strength of evidence [14; 15]. The application of likelihood ratios in glass evidence [16] and fire debris analysis [7; 8] is increasingly used in academic research.