Bayesian melding is a special case of multivariate Bayesian inference in which the variables follow some known theoretical relationship. Here Bayesian melding techniques are extended to stochastic theoretical relationships where they previously functioned only for deterministic relationships. The extension to the stochastic case requires new methods for both the selection and updating of Bayesian priors. We draw analogy to the deterministic Bayesian melding in Poole and Raftery (2000) to discuss prior selection, and propose a technique that can be used in the more general case. We then build upon Sevcikova, Raftery, Waddell (2007) to provide a complementary method for Bayesian updating. Using the new Bayesian melding techniques, we show how inference can be obtained on variables that are subject to Agent Based models. This is significant for Agent Based modelling as it provides a more rigorous framework for parameter selection. These concepts are demonstrated with a worked example.