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Unit information: Bayesian Modelling B 34 in 2016/17

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Unit name Bayesian Modelling B 34
Unit code MATHM0024
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2C (weeks 13 - 18)
Unit director Professor. Jonty Rougier
Open unit status Not open
Pre-requisites

Applied Probability 2 (MATH 21400), Bayesian Modelling A (MATH 34910)

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

Description

Much of the real advantage of the Bayesian approach to statistical modelling and inference is only seen when dealing with the slightly more complex situations encountered in this unit. Hierarchical models allow us to model situations where we simultaneously analyse different groups of data and where the parameters describing the groups can be assumed to be similar, using 'graphical keep track of the different kinds of variation. We will discuss how to draw inference in such models, and then how to actually do that in practice, leading to discussion of Markov chain Monte Carlo (MCMC) techniques, which are powerful and elegant algorithms based on simple ideas of conditional probability. Graphical modelling and MCMC are the basis for a package called WinBugs for doing Bayesian analysis without needing to write your own program, and there will be demonstrations and some hands-on practice with using that package on range of interesting examples.

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

The unit is based on the same lectures as Bayesian Modeling B (MATH 34920), and has the same lectures and examinations as that unit. Students taking this unit, however, will be required to complete a mini-project that will be assessed as 20% of the final mark.

Further information on the unit can be found at:

http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html

Intended learning outcomes

The students will be able to:

  1. Represent complex data by means of a hierarchical model
  2. Display such a model graphically
  3. Understand and apply MCMC techniques for performing Bayesian analysis in practice
  4. Justify theoretically the use of the various algorithms encountered
  5. Use software programs to implement algorithsm covered in this unit

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.

Teaching details

Lectures, (theory and practical problems) supported by weekly formative homeworks, some of which involve computer practical work with R and WinBugs, and a mini-project.

Assessment Details

The assessment mark for Bayesian Modelling B is calculated from a 1½-hour written examination (80%) and a mini-project (20%).

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

Reading and References

Reading and references are available at: http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html

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