Bayesian Statistics (Level M) STATS5014
- Academic Session: 2023-24
- School: School of Mathematics and Statistics
- Credits: 10
- Level: Level 5 (SCQF level 11)
- Typically Offered: Semester 2
- Available to Visiting Students: Yes
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%)
Main Assessment In: April/May
■ 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.
Intended Learning Outcomes of Course
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.
Minimum Requirement for Award of Credits
Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.