This thesis investigates the interpretation of forensic evidence through the use of likelihood ratios (LRs), with a particular focus on the role of prior probabilities and LR distributions in forensic DNA analysis. In forensic science, LRs are commonly used to quantify the strength of evidence in favor of one hypothesis over another. However, challenges arise in practice due to the complexity of DNA mixtures and the necessity of integrating prior information in certain scenarios. The first part of this work explores when and how prior probabilities must be incorporated into LR calculations, demonstrating through theoretical exposition and case studies that neglecting priors or assuming equal priors can lead to misleading conclusions.

Two detailed case studies illustrate the impact of introducing new persons of interest (PoIs) and how prior knowledge about associations between individuals can alter posterior probabilities. A comparison is also drawn between categorical and probabilistic approaches in body fluid analysis, with the latter offering a more nuanced interpretation of mRNA profiling data.

In the second part, the thesis introduces methods to estimate LR distributions for DNA contributors. These include threshold-based and genotype sampling techniques, which are tested across synthetic mixtures with varying contributor ratios. Furthermore, the behavior of LRs is studied for relatives of the true donor.

The findings underscore the importance of transparently reporting assumptions about priors and the value of presenting LR tables to facilitate Bayesian reasoning by decision makers. Overall, the thesis contributes to a more robust and interpretable application of statistical reasoning in forensic science.