Multi-element comparisons of tapes evidence using dimensionality reduction for calculating likelihood ratios

Area of Science:

• Forensic Science
• Analytical Chemistry
• Statistics

Background:

• Computing likelihood ratios (LRs) for multi-element forensic evidence is challenging due to data complexity.
• Existing multivariate random effects models can be unstable and produce extreme LR values, especially with more variables.
• High-dimensional data in forensic analysis requires robust dimensionality reduction techniques.

Purpose of the Study:

• To evaluate a novel method combining principal component analysis (PCA) and post-hoc calibration for analyzing high-dimensional, multi-element forensic evidence.
• To assess the performance of this method in calculating and calibrating likelihood ratios (LRs) for electrical tape samples.
• To determine the optimal number of principal components (PCs) for accurate and reliable forensic comparisons.

Main Methods:

• Applied additive log-ratio transformation to 18-element electrical tape data (analyzed by LA-ICP-MS).
• Utilized scores of the first five principal components (PCs) as input for the likelihood ratio formula (LR MVN).
• Implemented a post-hoc calibration method to adjust calculated LRs for improved accuracy and range.

Main Results:

• Initial LR calculations yielded extreme values, necessitating post-hoc calibration.
• The calibrated LRs fell within an appropriate range, demonstrating the effectiveness of the calibration step.
• The scenario using the first five PCs (LR5) achieved the lowest false exclusion (2.2%) and false inclusion (3.7%) error rates, indicating optimal performance.

Conclusions:

• The proposed method effectively reduces dimensionality in multi-element forensic data, overcoming limitations of traditional approaches.
• PCA combined with post-hoc calibration provides a stable and reliable way to compute well-calibrated likelihood ratios.
• This approach enhances the accuracy of forensic comparisons, particularly for complex datasets like those from electrical tapes.