Unit information: Graphical Models in 2013/14

Unit name	Graphical Models
Unit code	MATHM6002
Credit points	10
Level of study	M/7
Teaching block(s)	Teaching Block 1 (weeks 1 - 12)
Unit director	Dr. Didelez
Open unit status	Not open
Pre-requisites	None
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including 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, economics and genetics, and students will be introduced to software for graphical modelling.

Aims

This unit is given in weeks 7-12 of Teaching Block 1

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, forensics, economics and genetics, and students will be introduced to software for graphical modelling.

Syllabus

Introduction to graphs and Markov properties. Graphical models for computations:

• exact computation with probability propagatio
• approximate computation with McMC
• Bayesian hierarchical models
• hidden Markov models

Graphical models for causal reasoning: causal effect, de-confounding etc. Learning graphical models (model search): some principles and algorithms.

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.

Intended Learning Outcomes

The students will be able to:

• Describe the language of graphical modelling.

• Construct directed acyclic graphs (DAGs) for statistical models.

• Identify properties of statistical models from the structure of the DAG.

• Demonstrate the usefulness of graphical models in Bayesian hierarchical models, expert systems, hidden Markov models, causal reasoning and model search.

• Formulate and fit graphical models using WinBUGS and elements of the gR family of R packages.

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.

Teaching Information

Lectures (theory and practical problems) supported by exercise sheets, some of which involve computer practical work with appropriate statistical packages.

Assessment Information

Assessment will be by means of homework exercises as well as an extended project (to be complete in weeks 13-14), in which graphical modelling is used to assess some data. The student will present a report describing the relevant graphical modelling theory, the model that was used to analyse the data, and the results of the analysis. The assessment criteria for the project will be based on a suitably modified version of the current Mathematics Department Project Assessment form. The written report will count for 90% of the assessment mark and the homework exercises will count for 10%. Both the written report and the exercises will be marked by the member of staff in charge of the unit together with an independent second marker.

Reading and References

• Cowell, Dawid, Lauritzen and Spiegelhalter. Probabilistic Networks and Expert Systems. Springer-Verlag, 1999.
• Gelman, Carlin, Stern and Rubin. Bayesian Data Analysis, Chapman & Hall/CRC, 2003.
• Gilks, Richardson and Spiegelhalter. Markov Chain Monte Carlo in Practice, Chapman & Hall, 1996.
• Lauritzen. Graphical Models, OUP, 1996.
• Pearl. Causality: Models, Reasoning and Inference, CUP, 2000.
• Whittaker. Graphical Models in Applied Multivariate Statistics, Wiley, 1990.