Score-based likelihood ratios and sparse Gaussian processes

Abstract

This thesis concerns two main topics: score-based likelihood ratios (SLRs) for the evaluation of the strength of forensic evidence, and knot selection in sparse Gaussian processes. The work on the first topic seeks to theoretically and empirically justify the use of SLRs in court in place of full, feature-based likelihood ratios (LRs) which are rarely possible to calculate. We show that while the discrepancy between an SLR and the true LR can be unbounded, general probabilistic bounds on an LR given a score exist. These bounds show that the SLR will usually behave reasonably, and will tend to yield the same categorical decisions as the use of the full LR. We also study the problem of selecting a score in the case that the population of sources that possibly generated the relevant evidence of unknown origin is finite. We propose a bivariate performance measure of a score that directly ties to the sufficiency of the score for the forensic hypothesis in question. We then show that the most common scores, measures of dissimilarity between two pieces of evidence, can typically be improved via a general strategy for modifying the score function. We also propose a method to aggregate scores, partially addressing the problem of selecting a score function, via sparse GPs. Thus, we find an application of the second topic in this dissertation to the first topic. Finally, two chapters are dedicated to the study of a proposed method of efficient knot selection in sparse Gaussian processes. Our algorithm is applicable to many types of data and several different objective functions or inferential algorithms. We demonstrate that our algorithm can appropriately select the number and locations of knots so that the resulting predictions are competitive with both a full Gaussian process and models resulting from the currently standard knot selection methods. However, our algorithm tends to train models several times faster. Our algorithm is successfully applied in the chapter on score selection and aggregation for SLRs.