A common question in forensic analysis is whether two observed data sets originate from the same source or from different sources. Statistical approaches to addressing this question have been widely adopted within the forensics community, particularly for DNA evidence, providing forensic investigators with tools that allow them to make robust inferences from limited and noisy data. For other types of evidence, such as fingerprints, shoeprints, bullet casing impressions and glass fragments, the development of quantitative methodologies is more challenging. In particular, there are significant challenges in developing realistic statistical models, both for capturing the process by which the evidential data is produced and for modeling the inherent variability of such data from a relevant population.

In this context, the increased prevalence of digital evidence presents both opportunities and challenges from a statistical perspective. Digital evidence is typically defined as evidence obtained from a digital device, such as a mobile phone or computer. As the use of digital devices has increased, so too has the amount of user-generated event data collected by these devices. However, current research in digital forensics often focuses on addressing issues related to information extraction and reconstruction from devices and not on quantifying the strength of evidence as it relates to questions of source.

This dissertation begins with a survey of techniques for quantifying the strength of evidence (the likelihood ratio, score-based likelihood ratio and coincidental match probability) and evaluating their performance. The evidence evaluation techniques are then adapted to digital evidence. First, the application of statistical approaches to same-source forensic questions for spatial event data, such as determining the likelihood that two sets of observed GPS locations were generated by the same individual, is investigated. The methods are applied to two geolocated event data sets obtained from social networks. Next, techniques are developed for quantifying the degree of association between pairs of discrete event time series, including a novel resampling technique when population data is not available. The methods are applied to simulated data and two real-world data sets consisting of logs of computer activity and achieve accurate results across all data sets. The dissertation concludes with suggestions for future work.

Digital image forensics is a field encompassing camera identication, forgery detection and steganalysis. Statistical modeling and machine learning have been successfully applied in the academic community of this maturing field. Still, large gaps exist between academic results and applications used by practicing forensic analysts, especially when the target samples are drawn from a different population than the data in a reference database.

This thesis contains four published papers aiming at narrowing this gap in three different fields: mobile stego app detection, digital image steganalysis and camera identification. It is the first work to explore a way of extending the academic methods to real world images created by apps. New ideas and methods are developed for target images with very rich flexibility in the embedding rates, embedding algorithms, exposure settings and camera sources. The experimental results proved that the proposed methods work very well, even for the devices which are not included in the reference database.