In this talk I discuss Bayesian Inference as a problem in Free Energy Minimization and the Fenchel-Legendre Duality related to this viewpoint . I specialize this to the estimation problem for nonlinear diffusions with nonlinear observations and show how this gives a stochastic control interpretation for the nonlinear estimation problem . Finally, I discuss how Shannon's Noisy Channel Coding Theorem could be viewed as a Bayesian Inference problem and demonstrate its similarities to the Gibbs variational Principle.