Abstracts Category : Other

Development and Properties of Kernel-based Methods for the Interpretation and Presentation of Forensic Evidence

by Douglas Armstrong

The inference of the source of forensic evidence is related to model selection. Many forms of evidence can only be represented by complex, high-dimensional random vectors and cannot be assigned a likelihood structure. A common approach to circumvent this is to measure the similarity between pairs of objects composing the evidence. Such methods are ad-hoc and unstable approaches to the judicial inference process. While these methods address the dimensionality issue they also engender dependencies between scores when 2 scores have 1 object in common that are not taken into account in these models. The model developed in this research captures the dependencies between pairwise scores from a hierarchical sample and models them in the kernel space using a linear model. Our 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, we can: 1) model very high-dimensional data when other methods fail; 2) determine the source of multiple samples from a single trace in one calculation. Our model can be used to address high-dimension model selection problems in different situations and we show how to use it to assign Bayes factors to forensic evidence. We will 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. Advisors/Committee Members: Cedric Neumann.