We demonstrate that Bayesian networks fill a significant methodology gap for uncertainty quantification in particle physics, providing a framework for modeling complex systems with physical constraints. To address the problem of interaction position reconstruction in dark matter direct-detection experiments, we built a Bayesian network that utilizes domain knowledge of the system in both the structure of the graph and the representation of the random variables. This method yielded highly informative per-interaction uncertainties that were previously unattainable using existing methodologies, while also demonstrating comparable precision on reconstructed positions.