The DNA technology applied to forensic science has improved significantly in recent years. As a result of these advancements, DNA profiles can be generated from a low-template amount of DNA. This advancement, however, can lead to more complex mixtures due to the instrumentation picking up trace amounts of DNA. This leads to the need for these more challenging profiles to be interpreted. Due to the lack of standardization in DNA profile interpretation, one complex DNA profile is likely to draw several different conclusions from DNA analysts when assessing the number of contributors (NoC). Probabilistic genotyping software (PGS) is a possible solution to the problems of complex DNA profile interpretations. DNA-View® Mixture Solution™, developed by Dr. Charles Brenner, is a continuous modelling PGS that considers genotypes, peak height, stutter, dropout, and other artifacts that result from stochastic effects in the interpretation of DNA profiles. Mixture Solution has the potential to minimize some of the uncertainty inherent in DNA analysis of profiles having multiple contributors. In this project, DNA mixture analysis with Mixture Solution was applied to two and three-person mixtures having ratios ranging from 1:1 to 8:1 and 1:1:1 to 8:1:8. Two scenarios with several hypotheses were tested regarding each contributor as if they were the person of interest (POI) in a real case. Mixture Solution assigns the most favorable hypothesis for and against the POI and calculates an LR representing the comparison of those two hypotheses. In the final reports, trends previously observed in two-person mixture ratios were also observed in three-person mixtures. The main factor driving low LR assignment in three-person mixtures is low template DNA. Low peak heights and dropout are the factors driving low LR assignment. The factors that make manual DNA profile interpretation challenging can also challenge PGS. However, the robustness of Mixture Solution was demonstrated throughout the project with complex three-person mixtures.

Using computer systems for probabilistic genotyping on DNA evidence in forensic casework is beneficial as it allows a complete analysis of the data available for a wide range of profiles, a range that is limited when analyzed manually. One such software, Bulletproof, uses the exact method as the statistical foundation of its web-based interface to estimate the likelihood ratio of two hypotheses that explain the given evidence. In this investigation, the capability of Bulletproof was examined by analyzing the effects of evidence and reference sample template amount, injection time, and stutter filter utilization on likelihood ratio. In terms of likelihood ratio, deconvolution by the software is more efficient in cases in which evidence samples of high contrast ratios (such as 1:9 vs. 1:1) and low contributor count have high template, and when sample injection times are low. Reference sample template amount and injection time are less impactful than that of evidentiary samples. As with unknown samples, reference samples should be analyzed beforehand and artifacts removed for better deconvolution.

DNA samples are a part of the collected physical evidence during the comtemporary crime scene investigation procedure. After processing the samples, a laboratory obtains short tandem repeat electropherograms. In case of mixed DNA profiles, i.e., profiles that contain DNA material from more than one contributor, the laboratory needs to estimate the test statistic (likelihood ratio) that could provide evidence, either inculpatory or exculpatory, against the person of interest. This is automated with probabilistic genotyping (PG) software with (fully-)continuous models: the ones that consider the heights of the observed peaks. In this thesis, we provide understanding of the modern PG methods. We then show how to improve measurable indicators of the algorithm performance, such as precision and inference runtime, that directly correspond to the efficiency and efficacy of work performed in a lab. With quicker algorithms the forensics laboratories can process more samples and provide more comprehensive results by reanalysing the mixtures with different hypotheses and hyperparameterisations. With more precise algorithms, there will be a grater confidence in their results. The precision of the solution would ameliorate the admissibility of the provided evidence and reliability of the results. We achieve improvements over the state-of-the-art by utilising probabilistic programming and modern Bayesian inference methods. We describe a differentiable (and hence continuous) continuous model that can be used with different estimators from both the sampling and variational families of techniques. Finally, as the different PG products output different likelihood ratios, we provide explanation of some of the factors causing this behaviour. This is of high importance because if two solutions are used for the same crime case, the difference must be understood. Otherwise, because of lack of consensus, the results would cause confusion or, in the worst case, would not be admitted by the court.