Validation of a feature-based likelihood ratio method for the SAILR software. Part I: Gas chromatography–mass spectrometry data for comparison of diesel oil samples

Abstract Statistical modelling of probability distributions from background data to arrive at a likelihood ratio (LR) is becoming more common in the forensic community. An open-source software called SAILR was recently launched by a European Union-funded project to provide forensic practitioners with a mathematical backbone in a user-friendly graphical interface. Before presenting values produced by the software as evidence in court, the LR method must be validated. In this study, a multivariate feature-based LR method for SAILR was validated using gas chromatography-mass spectrometry data from comparison of diesel oil samples. The validation strategy relied on use of specific performance characteristics (e.g., accuracy, discrimination, and calibration) and their corresponding metrics (e.g., cost of log-likelihood ratio and equal error rate). The validation also encompassed the normality assumption for within-source variation. Any deviation from the normality assumption was mitigated using Lambert W transformation of the data, which improved model performance. The LR method chosen for validation was optimized using background data, and a baseline method was simultaneously developed to provide the validation criteria. The results showed that the available data could support a trivariate (or lower) model. The LR method chosen for validation outperformed the baseline method according to the performance characteristics. Using the empirical lower and upper boundaries LR method, the output limits were determined to be 1/537 ≤ LR ≤ 1412. By passing the tests of normality and the validation criteria, the method was considered valid within this LR range for data of sufficient quality, and relevant to the background data set.