Contributions to ROC Curve and Likelihood Ratio Estimation for Forensic Evidence Interpretation



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Biometric traits such as faces and fingerprints are critical in forensic evidence interpretation. There has been a growing interest to study the repeatability, reproducibility, and accuracy of modalities for forensic evidence interpretation since the 2009 National Research Council report and the more recent report from the 2016 President's Council of Advisors on Science and Technology. In this dissertation, we investigate two statistical methods for forensic evidence interpretation, which are score-based likelihood ratio (SLR) and receiver operating characteristic (ROC) curve. In the first part of this dissertation, we investigate the repeatability and reproducibility of three existing statistical methods for estimating the SLR including parametric estimation, kernel density estimation, and recently adopted logistic regression estimation. We perform extensive simulations and used different face and fingerprint biometric datasets to investigate the repeatability and reproducibility of the existing SLR estimation methods. We also provide a parametric way to estimate the variance of the SLR based on the ROC curves. Simulation studies and real studies are provided to indicate the usefulness of the variance estimation method. In the second part, we consider modeling of ROC curves using both the order constraint and covariates associated with each score given that the latter (e.g., demographic characteristics of the underlying subjects) often have a substantial impact on discriminative accuracy. The proposed method is based on the indirect ROC regression approach using a location-scale model, and quadratic optimization is used to implement the order constraint. The statistical properties of the proposed order-constrained least squares estimator are studied. Several situations are discussed in the simulation studies, including multiple covariates, non-Gaussian random samples, and heteroscedastic modeling. The results of the simulation studies corroborate the superior performance of the proposed approach. Its practical usefulness is demonstrated applying face recognition data from the “Good, Bad, and Ugly” face challenge, a domain in which accounting for covariates has hardly been studied.