Unit name | Bayesian Modelling B |
---|---|
Unit code | MATH34920 |
Credit points | 10 |
Level of study | H/6 |
Teaching block(s) |
Teaching Block 2C (weeks 13 - 18) |
Unit director | Dr. Yu |
Open unit status | Not open |
Pre-requisites | |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
This unit will develop on the material covered in Bayesian Modelling A, and will provide the necessary background, experience and modern computational tools to apply Bayesian modelling techniques to realistic applications. The course will start with a gentle introduction to the basic principles of Monte Carlo techniques, with examples of applications in science. The elegance, simplicity and power of the concepts will motivate their use in the context of Bayesian inference. The course will then focus on Markov Chain Monte Carlo and Sequential Monte Carlo techniques. These methods have revolutionised statistical inference over the last 10 - 15 years. The application of these powerful tools will be gradually introduced and illustrated with practical examples from various fields of science, including finance, telecommunications, biology, and nuclear science.
Aims
This unit will develop on the material covered in Bayesian Modelling A, both by extending the range of models considered to include hierarchical specifications, and by deriving probabilistic algorithms that enable the practical use of Bayesian methods in a very broad range of applications.
Syllabus
Hierarchical models; Directed acyclic graphs; Markov chain Monte Carlo; Gibbs sampler; Metropolis-Hastings algorithm; Application to analysing data, and posterior summaries.
Relation to Other Units
This unit is currently also available at Level 7. However 2011/12 is the last year in which this option is available. From 2012/13 the unit will only be available at Level 6.
The Level 7 units that build on the methods and knowledge discovered in Bayesian Modelling B are Monte Carlo Methods (M6001) and Graphical Modelling (M6002).
The students will be able to:
Transferable Skills:
In addition to the general skills associated with other mathematical units, you will also have the opportunity to gain practice in the following: computer literacy and general IT skills, use of R and WinBugs as programmable statistical packages, interpretation of computational results, time-management, independent thought and learning, and written communication.
Lectures (theory and practical problems) supported by example sheets, some of which involve computer practical work with R and WinBugs.
The assessment mark for Bayesian Modelling B is calculated from a 1½-hour written examination in May/June consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators are NOT permitted to be used in this examination.
The following texts may be useful for reference: