Extreme Value Theory

A flooded British road

Extreme Value Analysis is a branch of statistics that develops statistical methodology for the unusually large or small observations in a data set. It is fundamentally linked to Extreme Value Theory, which is a branch of probability focusing on the asymptotic tail behaviour of probability distributions and stochastic processes.

Why should we care about extreme events?

Extreme events, though rare, almost always have disastrous and long-term impacts across different sectors of society and different economic sectors. The two main application domains for EVA are natural hazards and financial risk management. Examples of natural hazards include fluvial or coastal flooding, droughts, heat waves, and severe storms. Examples in finance include stock market crashes and large insurance claims. In all cases, prediction of the risk of future extreme events is a vital step in enabling us to mitigate the effects of such catastrophic events. Because extreme events are rare, it is impossible to predict this risk from historical data alone and a suitable model fitted to historical data must be used for the necessary extrapolation.

Why do we need special methodology?

Almost all standard statistical methods characterise the mean behaviour of a process or data sample and are therefore not generally useful for capturing tail behaviour. To mitigate the impact of the mean behaviour on tail extrapolation, methods which focus specifically on tail events are required.

What do we do?

Our group is interested in many different aspects of extreme value analysis, with research and publications covering theory, methodology and application. Often our projects cover more than one of these areas and we also work directly with other statistical research groups to facilitate cross-pollination of ideas across statistical disciplines. There is a particularly strong link with the Environmental and Ecological group.

Current methodological research areas:

  • Development of new dependence models for multivariate and spatial extremes, with focus on efficient and flexible modelling and inference for high-dimensional spatio-temporal data;
  • Creation of methodology for the extremes of complex processes, including identification and incorporation of trends, extreme event drivers and temporal dynamics;
  • Statistical downscaling of extreme events from the gridded output of mathematical or numerical models, e.g. global climate, hindcast and forecasting models;
  • Compound extreme event modelling.

Current application areas:

  • Flooding: development of spatial and temporal models for river and coastal flooding, and estimation of flood risk in a changing world;
  • Extreme metocean environments: estimation of risk, and associated uncertainty quantification, in , including how these fluctuate over space-time, or with changes in physical drivers;
  • Earthquakes: estimating the scale of future extreme earthquakes that arise either from gas extraction or from carbon capture storage programmes;
  • Maintenance scheduling: long-term optimising time windows for undertaking maintenance of structures such as wind-farms and estuary barriers (e.g., Thames Barrier) to minimise the chance of extreme events during the scheduled works.
  • Downscaling of natural hazards: examples include temperature, air pollution and extreme ocean environments;
  • Ground-based effects of extreme space weather events: understanding the spatio-temporal behaviour of, and risk, from different types of solar storms;
  • Air pollution: forecasting the risk of episodes of poor air quality and understanding within-episode behaviour.

As well as links with multiple universities in the UK and abroad, the group has strong research links with many collaborators both in the industry and in research organisations. The majority of the collaborators are experts in one or more of the fields detailed above. Organisations/groups with whom we have links include Shell, EDF, JBA Trust, British Geological Society, Centre for Ecology and Hydrology (Wallingford), Lancaster Environment Centre, UK Meteorological Office, HR Wallingford, National Oceanographic Centre.


The impact of the research work of our group is substantial. It has been used in:

  • Optimising the height of all coastal flood protection schemes in the UK, influencing a total spend of £0.9B on 900 schemes over the period 2008-13 and with the methods still being used;
  • Providing input and analysis to the Government’ 2016 National Flood Resilience Review, following the extensive flooding of December 2015, to assess spatial risk of flooding in multiple rivers and to estimate the risk of flooding occurring somewhere in the country in a year;
  • Providing spatial flood risk scenarios for the Government’s 2016 National Risk Assessment.
  • Giving insurance companies with their first tool to assess their aggregated financial loss from widespread flooding;
  • Presenting evidence of fundamental importance on the likely cause of the 1980 sinking of the MV Derbyshire, the largest UK ship ever to have sunk, to the £11M High Court Reopened Formal Investigation. Until the High Court Investigation, the reasons for its sinking. Our statistical analysis was key to the investigation and was treated as the fundamental evidence in the Judge's conclusions;
  • Specifying new worldwide mandatory design standards for bulk carriers, ore carriers and combination carriers. Specifically, the strength of hatch covers has been increased by 35% from the previous design standards. In 2008-13 this impacted on the design of 1720 new bulk carriers, and resulted in strengthening as well as new inspection and maintenance procedures for 5830 existing bulk carriers. The design standards are still being used.
  • Contributions to the development of best practice for the design and re-assessment of fixed and floating offshore structures worldwide over many years, with 5-year nett present value of the order of £100 million.

Case study: Eleanor D'Arcy

Eleanor is a PhD student at the EPSRC funded STOR-i CDT and organises the extremes research group at Lancaster University. Her PhD project concerns is titled ‘Extreme Value Methods for Protecting and Maintaining Critical Infrastructure from Natural Hazards.’ Eleanor’s PhD is in collaboration with EDF Energy research and development, sitting in the natural hazards and environment team for nuclear safety.

In her PhD so far, she has developed a methodology for extreme sea level estimation that accounts for seasonality, temporal dependence and climate change. Obtaining accurate sea level return level estimates is crucial for coastal flood defence management, especially for nuclear power plants. By incorporating spatial information, she was able to improve the method for uncertainty quantification associated with return level estimates. Her results are a major improvement on those currently used in practice and Eleanor’s work will be adopted in the upgraded Environment Agency Coastal Flood Boundary Report to provide updated extreme sea level estimates nationwide. This work is published across two papers; both can be found via her website.

Eleanor is particularly interested in scientific communication and outreach. She recently won the TakeAIM competition, organised by the Smith Institute, where she presented the importance of extreme value statistics on the industrial stage. Additionally, she was a finalist in the STEM for Britain 2022 competition where she presented her research at the House of Commons. Eleanor has been appointed as a William Guy Lecturer for the 2023/24 academic year, where she will highlight the crucial role that statistics, particularly extreme value analysis, plays in our fight against climate change for sixth-form students across the UK.

Eleanor D'Arcy