Module Catalogue 2026/27

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

This module introduces a technique which performs a seemingly impossible task: to predict the probability of events that are more extreme than any that have happened before. Although these methods have been around for over 70 years, their application in complex real-life problems has only recently been developed. For example, the governmental coastal flood defence division employs statisticians using these methods to calculate the required height of sea-walls to prevent flooding. Extreme value theory is also used to help engineers decide how strong to build bridges or oil rigs and to model excessively high pollution levels.

Outline Of Syllabus

Extremal Types Theorem, the Generalised Extreme Value distribution (GEV), likelihood and estimation for the GEV, its uses and limitations. Alternative extreme value characterisations: the distribution of extreme r-order statistics; the Generalised Pareto Distribution. Application to real problems: temporal dependence and non-stationarity in data on extremes. Issues involved in extreme value modelling of environmental and other data. Multivariate extremes: dependence structures and practical applications.

Students will acquire skills in analysing relevant statistical models for data on extremes both from a theoretical and data analytic viewpoint. Students will appreciate the practical application of these methods in areas such as climate science, meteorology and engineering.

Intended Knowledge Outcomes

At the end of the module it is expected that a student will be able to:
- Outline the fundamental principles and concepts of extreme value theory (EVT).
- Describe the properties of the Generalised Extreme Value (GEV) distribution and apply this model to block maxima.
- Explain the use of the Generalised Pareto Distribution (GPD) in threshold models.
- Describe common modelling issues arising from the analysis of extremes, and methods to circumvent these issues.
- Discuss multivariate extremes and their dependence structures.
- Summarise conditional modelling approaches for extreme values.

Intended Skill Outcomes

At the end of the module it is expected that a student will be able to:
- Apply the methods delivered throughout the course to real-world data.
- Implement appropriate statistical analyses in R.
- Validate and assess the fit of extreme value models through appropriate statistical tests and diagnostics.
- Interpret the fit of extreme value models to real-world data, including contextual reporting of findings.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem classes are used to help develop the students’ abilities at applying the theory to solving problems.

The teaching methods are appropriate to allow students to develop a wide range of skills. From understanding basic concepts and facts to higher-order thinking.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem-solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; the summative assessment has a secondary formative purpose as well as its primary summative purpose.

Note: the exam for MAS8610 is more challenging than the exam for MAS3921.

General Notes

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