Unit name | Graphical Models |
---|---|
Unit code | MATHM6002 |
Credit points | 10 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 2C (weeks 13 - 18) |
Unit director | Dr. Didelez |
Open unit status | Not open |
Pre-requisites | |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit aims
This unit will introduce the theory of graphical modelling for complex statistical models, and will cover the practical use of this theory in several areas including, but not necessarily limited to: Bayesian hierarchical modelling, hidden Markov models, and causality. Examples will be drawn from diverse areas including finance, medicine, forensics, economics and genetics, and students will be introduced to software for graphical modelling (working knowledge of the software R is a prerequisite).
General Description of the Unit
For complex statistical models it is helpful to lay out all the variables of interest in a diagram. The resulting graphical model then becomes a useful tool for understanding the relationships between different parts of the model, and helps to suggest techniques for analysis. This unit will study the theory of graphical modelling and apply it to several areas of interest, including:
using graphical models to facilitate and accelerate computations: complex highdimensional models arise for example in form of expert systems, where the relationships between factors reflect experts' knowledge, or in the context of Baysian hierarchical modelling. Both types of models are very naturally expressed using graphical models and the graphical structure can be exploited to simplify complex computations. using graphical models for causal reasoning and inference: having a glass of red wine per day is correlated with a reduced risk of heart disease, but is the red wine really causing the reduced risk, or is it simply also a symptom of some other causal factor? In this course causality will also be studied using the language of graphical models. searching for (graphical) structure: in many applications, e.g. genetics, it is the dependence structure among variables or factors itself that is of interest. When represented graphically, the model search can be carried out in a systematic and easy to intepret fashion. Several software packages exist for investigating graphical models. Students on this course will learn to use one of these packages (Hugin, WinBUGS, gR or GRAPPA) to perform inference on graphical models.
Relation to Other Units
This unit requires a basic background in probability and statistics, but no prior graph theory is needed. Parts of this unit will refer to Bayesian analysis so that some prior knowledge in this topic will be helpful. An ability and willingness to carry out a considerable amount of programming is assumed.
Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/
Learning Objectives
The students will be able to:
Transferable Skills
Computing, critical thinking especially regarding causal reasoning, and the ability to give precise mathematical formulations to a variety of problems. Furthermore, writing skills, i.e. the ability to report findings in a coherent report.
Lectures (theory and practical problems) supported by exercise sheets, some of which involve computer practical work with appropriate statistical packages.
100% Coursework.
The coursework will be marked against the criteria on the 0-100 scale.