This course introduces methods of modern Bayesian inference, with an emphasis on practical issues and applications.

16 lectures (1 or 2 each week)

4 1-hour tutorials

5, 2-hour computer-based practicals

STATS4041 Bayesian Statistics

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

■ To develop the foundations of modern Bayesian statistics;

■ to demonstrate how prior distributions are updated to posterior distributions in simple statistical models;

■ to formulate, analyse and interpret hierarchical models, fitting them using either WinBUGS, Stan, or R;

■ to demonstrate how decision making is performed in Bayesian framework.

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

■ Describe the rules for updating prior distributions in the presence of data, and for calculating posterior predictive distributions;

■ Derive posterior distributions corresponding to simple low-dimensional statistical models, typically, but not exclusively, with conjugate priors;

■ Describe and compute various summaries of the posterior distribution, including posterior mean, MAP estimate, posterior standard deviation and credible regions (including HPDRs) and the predictive distribution;

■ Explain different approaches to the choice of prior distribution;

■ Explain the role of hyperparameters in Bayesian inference, introduce them appropriately into statistical models and use the empirical Bayes approach for their determination;

■ Explain the use of independent simulation techniques for posterior sampling and apply them in simple contexts using R;

■ Formulate and analyse simple hierarchical models using Gibbs sampling in either WinBUGS, Stan, or R;

■ Describe and apply simple checks of mixing, and explain when mixing is likely to be poor;

■ Explain the role of decision theory in Bayesian analysis, formulate the decision process mathematically, and prove simple results.

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