This course develops advanced topics in modern Bayesian statistics, including both the underlying theory and related practical issues.

20 lectures (typically 2 each week for 10 weeks of Semester 1)

4 1-hour tutorials

2 2-hour computer-based practicals

STATS 5013 Advanced Bayesian Methods (Level M)

None

90-minute, end-of-course examination (100%)

To introduce students to advanced stochastic simulation methods such as Markov-chain Monte Carlo in a Bayesian context;

to illustrate the practical issues of application of such methods, with real data examples;

to discuss Bayesian approaches to model selection, model criticism and model mixing.

By the end of this course students will be able to:

■ Illustrate the use of Monte Carlo methods, including importance sampling;

■ Explain the operation and basic theory of the two main Markov-Chain Monte-Carlo methods, Gibbs sampling and the Metropolis-Hastings algorithm;

■ Derive the full conditional distributions for parameters in simple low-dimensional problems;

■ Implement Gibbs sampling and the Metropolis-Hastings algorithm in R;

■ Apply diagnostic procedures to check convergence and mixing of MCMC methods

■ Describe Bayesian approaches to model selection;

■ Calculate Bayes' factors for simple model comparisons;

■ Explain MCMC approaches to model selection and model mixing;

■ Describe posterior predictive checks as a means of model criticism.