This study explores the development and properties of kernel-based methods for the interpretation and presentation of forensic evidence.
The kernel-based method developed in this study for the interpretation and presentation of forensic evidence captures the dependencies between pairwise scores from a hierarchical sample and models them in the kernel space using a linear model. This model is flexible to accommodate any kernel satisfying basic conditions and as a result is applicable to any type of complex high-dimensional data. An important result of this work is the asymptotic multivariate normality of the scores as the data dimension increases. As a result, the authors can model very high-dimensional data when other methods fail and determine the source of multiple samples from a single trace in one calculation. This model can be used to address high-dimension model selection problems in different situations, and the authors show how to use it to assign Bayes factors to forensic evidence. The authors provide examples of real-life problems using data from very small particles and dust analyzed by SEM/EDX and colors of fibers quantified by microspectrophotometry.