A unifying framework for the modelling and analysis of STR DNA samples arising in forensic casework

This paper presents a new framework for analysing forensic DNA samples using probabilistic genotyping. Specifically it presents a mathematical framework for specifying and combining the steps in producing forensic casework electropherograms of short tandem repeat loci from DNA samples. It is applicable to both high and low template DNA samples, that is, samples containing either high or low amounts DNA. A specific model is developed within the framework, by way of particular modelling assumptions and approximations, and its interpretive power presented on examples using simulated data and data from a publicly available dataset. The framework relies heavily on the use of univariate and multivariate probability generating functions. It is shown that these provide a succinct and elegant mathematical scaffolding to model the key steps in the process. A significant development in this paper is that of new numerical methods for accurately and efficiently evaluating the probability distribution of amplicons arising from the polymerase chain reaction process, which is modelled as a discrete multi-type branching process. Source code in the scripting languages Python, R and Julia is provided for illustration of these methods. These new developments will be of general interest to persons working outside the province of forensic DNA interpretation that this paper focuses on.