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%)

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

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.

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