Abstract: A variational inference engine for probabilistic graphical models is disclosed. In one embodiment, a method includes inputting a specification for a model that has observable variables and unobservable variables. The specification includes a functional form for the conditional distributions of the model, and a structure for a graph of model that has nodes for each of the variables. The method determines a distribution for the unobservable variables that approximates the exact posterior distribution, based on the graph's structure and the functional form for the model's conditional distributions. The engine thus allows a user to design, implement and solve models without mathematical analysis or computer coding.