After describing the fundamentals of Bayesian inference, this course will examine the specification of prior and posterior distributions, Bayesian decision theoretic concepts, the ideas behind Bayesian hypothesis tests, model choice and model averaging, and evaluate the capabilities of several common model types, such as hierarchical and mixture models. An important part of Bayesian inference is the requirement to numerically evaluate complex integrals on a routine basis. Accordingly this course will also introduce the ideas behind Monte Carlo integration, importance sampling, rejection sampling, Markov chain Monte Carlo samplers such as the Gibbs sampler and the Metropolis-Hastings algorithm, and use of the Stan posterior simulation software.
The intended audience of this course is wide-ranging, from statistics and data science students to economics, actuarial, computer science and natural science (e.g. biology, geology, physics) students. Prior knowledge of basic probability is necessary, and knowledge of stochastic processes will be advantageous but is not required. The purpose of this course is to introduce students to Bayesian statistical concepts not seen in core courses which are primarily focused on frequentist statistics.
This course is jointly taught at two levels. MATH3871 is for 3rd year undergraduates, whereas MATH5960 is for Honours & Masters students. Lectures will be conducted simultaneously for both streams, but tutorial classes and computer labs will be conducted separately for the two groups and assessments may differ The lectures run from Weeks 1 to 10, and the combined tutorial/lab sessions run after the weekly lectures (Weeks 2 to 10). Students should bring their laptops to the tutorials so that they can complete the coding exercises.
