An exposure (treatment or risk factor) may affect an outcome of interest through a multitude of possible pathway. Some pathways may be direct in that they do not require the triggering of a mediating factor of interest by the exposure, while other pathways are through this mediating factor of interest. Using the principal stratification framework for causal inference (Frangakis and Rubin 2002), we develop a Bayesian approach for estimating direct and mediated effects in the context of a dichotomous mediator and dichotomous outcome, which is challenging as many parameters cannot be fully identified. Since likelihood theory is not well-developed for non-identifiable parameters, we consider a Bayesian approach which allows the direct and mediated effects to be expressed in terms of the posterior distribution of the population parameters of interest. This range can be reduced by making further assumptions about the parameters that can be encoded in prior distribution assumptions.