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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 catestrophic 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 methodology for analysing extreme values, helping to ensure that we can get the most information from these naturally scarce data. This includes 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 applications-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 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 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 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-termporal 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 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.

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