Extreme Value Statistics

Extreme events, though rare, can have an enormous negative impact on individuals, society, business, economies and infrastructure.

Examples of extreme events include river or coastal flooding, droughts and heatwaves, and stock market crashes. Prediction of the risk from future extreme events is therefore vital in enabling us to mitigate the effects from such catastrophic events. For example, engineers can use estimated flood risk to design appropriate flood defences.

Since extreme events are rare by definition, prediction of future events relies on extrapolation from a suitable model fitted to historical data. Extreme value analysis provides a statistical framework for this kind of analysis. In an extreme value analysis, extreme events are defined to be those observations in a sample which are unusually high, or low, and are therefore considered to occur in the tails of a probability distribution. Standard statistical methods are designed to characterise the mean behaviour of a process or data sample and are therefore not generally useful for capturing this tail behaviour. Subsequently, methods which focus specifically on tail events are required. Here at Lancaster, we are interested in many different aspects of extreme value modelling, both from a methodological and an applied perspective. Further details of specific research interests can be found in the sections below.

Methods

Our group is very active in the development of a methodology for analysing extreme values, helping to ensure that we can get the most information from these naturally scarce data. This includes the development of new dependence models for multivariate and spatial extremes based on more realistic assumptions for the data, as well as methods for analysing extremes of non-stationary processes.

Applications

A large part of the research carried out by the Extremes group is application-driven, with environmental problems being at the core of much of this work. Such problems include:

  • Development of spatial and temporal models for river flooding, and estimation of flood risk in a changing world;
  • Prediction of extreme coastal flooding;
  • Estimation of risk, and associated uncertainty quantification, in extreme Metocean environments;
  • Statistical downscaling of environmental variables, such as temperature and wave height, with a particular focus on extreme events;
  • Understanding the extremes of different characteristics of ocean environments, including how these fluctuate over space-time, or with changes in underlying physical variables;
  • Building physically-motivated statistical models of extreme storms;
  • Quantifying risk from, and changing the behaviour of, heatwaves;
  • Modelling spatial- and time-varying aspects of extreme space weather events.

The common challenges that arise from these and other environmental extreme events, such as droughts. include

  • The inclusion of knowledge about the physical process into the model;
  • Quantification and modelling of extremal dependence (in space and/or time);
  • Accounting for a temporal structure such as long-term trends and year-to-year variability.

As well as environmental applications, members of the group also carry out research into the extremes of financial and insurance data. Applications include:

  • Modelling volatility of the extremes of financial time series;
  • Quantifying joint dependence in high-dimensional financial series;
  • Understanding the mechanisms behind insurance claims linked to extreme weather events;
  • Quantifying inter-temporal variation of volatility using high-frequency time series.

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.

People

Academic Staff

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Extreme Value Statistics, STOR-i Centre for Doctoral Training

+44 (0)1524 593954 B28a, B - Floor, Fylde College

Extreme Value Statistics, Sustainable Catchments, Water Science

+44 (0)7866 715761

Extreme Value Statistics, STOR-i Centre for Doctoral Training

+44 (0)1524 593606 B80, B - Floor, PSC

Extreme Value Statistics, STOR-i Centre for Doctoral Training

+44 (0)1524 593965

Extreme Value Statistics

+44 (0)1524 594020 B42, B - Floor, Fylde College

Publications

Projects

Impact

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.