Dissertation - Open Access
Doctor of Philosophy (PhD)
Department / School
Mathematics and Statistics
Bayes factor, Evidence quantification, Forensic statistics, High-dimensional, Kernel method
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.
Library of Congress Subject Headings
Forensic sciences -- Statistical methods.
Bayesian statistical decision theory.
Includes bibliographical references (pages 220-224)
Number of Pages
South Dakota State University
Armstrong, Douglas, "Development and Properties of Kernel-based Methods for the Interpretation and Presentation of Forensic Evidence" (2017). Electronic Theses and Dissertations. 2175.