Document Type

Dissertation - Open Access

Award Date

2021

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

First Advisor

Christopher Saunders

Abstract

Many scholars have proposed the use of a Bayes factor to quantify the weight of forensic evidence. However, due to the complex and high-dimensional nature of pattern evidence, likelihood functions are intractable and thus, Bayes factors cannot be assigned using traditional methods. Approximate Bayesian Computation (ABC) model selection algorithms provide likelihood-free methods to assign Bayes factors. ABC Bayes factors leverage the use of the scoring functions commonly used in recent years in forensic statistics in a rigorous statistical manner. However, traditional methods for assigning ABC Bayes factors are subject of several criticisms. In this dissertation, one of the main criticisms of traditional ABC Bayes factors is alleviated by deriving a relationship between ABC Bayes factors and ROC curves. Additionally, the use of the ROC curve allows for an intuitive communication of the ABC Bayes factor. A simple example is outlined to illustrate the implementation of a ROC-ABC algorithm. Asymptotic properties of the ROC-ABC Bayes factor are explored. The ROC-ABC algorithm is implemented to quantify the weight of fingerprint evidence.

Number of Pages

180

Publisher

South Dakota State University

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Rights Statement

In Copyright