Bayesian methods will be employed to make inferences for stochastic processes, and this chapter will introduce the theory that is necessary in order to describe those procedures. The Bayes theorem, the foundation of the subject, is first introduced and followed by an explanation of the various components of the Bayes theorem: prior information; information from the sample given by the likelihood function; the posterior distribution, which is the basis of all inferential techniques; and lastly, the Bayesian predictive distribution. A description of the main three elements of inference, namely, estimation, tests of hypotheses, and forecasting future observations follows.