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

STATS4038 Advanced Bayesian Methods

90 - minute, end of course examination (85%)

Project (15%)

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;

to give students the opportunity to read further into one topic related to the course.

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;

■ Carry out a full Bayesian data analysis of a real data set by implementing MCMC methods and write a report to summarise their analysis and conclusions.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.