Bayesian Networks are probabilistic graph models that can be used for classification, prediction, diagnosis and parameter learning. Probabilities can be inferred from the models and missing values can be imputed, based on probability theory. Missing person cases place a strain on the already overstretched resources of Police Forces. Such cases predominantly come from at risk groups such as children in care and people suffering from depression or dementia. Current approaches for dealing with such cases are manual and rely upon empirical studies and domain knowledge. This paper proposes the use of a Bayesian Network model, which can be used to predict the likely location of a missing person (misper) for a number of at risk groups. The model is evaluated using a set of misper cases and results compare very favourably with those of the manual processes currently used by UK Police forces. The novel approach described provides both a theoretical foundation and a practical framework for the future development of a decision support system. In addition to the model, a contribution is made through guidelines, which recount experiences in learning a Bayesian Network from data.