If ML is to be responsibly applied to sensitive areas such as healthcare, banking or criminal justice, it is vital that its predictions treat every individual fairly. My research focuses on applying Bayesian statistical methods to this issue of fairness in ML. The core concept is ensuring every prediction made by the model aligns with the observed target distributions of all subgroups in the data. I test this alignment using Bayesian distributional inference to ensure the model generalizes to the population level. This framework is implemented via a Python algorithm that exhaustively checks every prediction on every subgroup to ensure consistency in an efficient manner.