After describing the fundamentals of Bayesian Inference this course will examine specification of prior distributions, links between Bayesian and frequentist inference, Bayesian model comparison and Bayesian computational methods. Markov chain Monte Carlo (MCMC) methods for computations will be described and implemented using statistical packages including WinBUGS. We will illustrate the advantages of the Bayesian approach be describing Bayesian inferential methods for a variety of models including linear models and various kinds of hierarchical structured models including mixture models.