Extreme Value Statistics Research at Lancaster

In all sorts of applications, accurate risk assessment relies on the effective evaluation of the extremal behaviour of the process under study. Unlike most of statistics which tries to say something about typical behaviour, Extreme Value Statistics attempts to characterise unlikely behaviour, or at least to say how unlikely the behaviour is. The research has a strong theoretical flavour, as the smoothness of physical processes means that they often satisfy natural mathematical conditions, and this mathematics is used to justify extrapolation to where there is little or no data. Methods for single variables are well established and in the Extreme Value Statistics Group at Lancaster, much research focuses on how to model joint extremes of more than one variable. This requires an adequate description of the extremal behaviour of the variables, which relies on understanding the dependence between extremal variables.

Applications include

• Offshore wave prediction;
• Flood risk assessment;
• Financial risk management;
• Insurance assessment;
• Setting industrial safety standards;
• Prediction of storm conditions.

Important methodologies

• Multivariate extreme value theory;
• Asymptotic theory motivating models;
• Spatial and temporal modelling;
• Characterising extremal dependence;
• Parametric and nonparametric modelling;
• Simulation based uncertainty assessment.

About the Extreme Values Group

The Department of Mathematics and Statistics at Lancaster hosts the internationally renowned Extreme Value Statistics research group. Group members are Jonathan Tawn, Emma Eastoe, Granville Tunnicliffe-Wilson and a variety of research students and postdoctoral researchers. We have strong collaborative links with other extreme value researchers around the UK, in Europe, the USA and beyond.

Interdisciplinarity

All of our theoretical research is motivated by close contact with applied researchers from the environmental and financial sciences and engineering. We work with hydrologists, climatologists, oceanographers, environmental chemists, economists, offshore engineers, and nuclear scientists among others.

Group research activities

Our current and recent research activities include

• Studying effect of climate change on extreme sea levels;
• Giving evidence to the Government enquiry into the sinking of the MV Derbyshire;
• Teaching postgraduate level courses in Extremes for PhD students from across the UK;
• Contributing to a study into Bulk Carrier safety for setting international safety limits for the design of these vessels;
• Risk assessment for nuclear reactors;
• Working with DEFRA on flood risk assessment for the whole UK coastline;
• Estimating trends in world record athletics performances;
• Optimising portfolio selection to protect against large loses;
• Predicting crashes of the stock market.

UK Extremes meeting

The next UK Extremes meeting will take place at Lancaster. Provisional dates have been set as 23rd-24th September 2008. A website with further details can be found here.

Extremes discussion group

This reading group meets regularly to discuss research papers of relevance to our work, and to share our research ideas.

Meetings calendar: 

4th February 2009, 3pm

Nason, G.P. and Silverman, B.W. The Discrete Wavelet Transform in S. J . Comp. and Graphical Statist.. 3, 163-191. Discussion by Idris.

7th January 2009, 4pm

Multivariate Extreme Value Methods in Finance. Presentation by Sawsan.

Methods for Multivariate Extremes. Presentation by Jon.

Dupuis, D. and Field, C.A. Robust estimation of extremes Canadian Journal of Statistics; Vol 21, pp 199-215. Discussion lead by Kanchan.

4th June 2008, 3.30pm

23rd April 2008, 3pm

Jonathan, P. and Ewans, K. Modelling the seasonality of extreme waves in the Gulf of MexicoProceedings of OMAE 2008. Presentation by Philip Jonathan.

Related departmental seminars

Some upcoming or recent departmental seminars with an extremes theme.

16th July 2008

Fabrizio Laurini

Robust statistic with the forward search with applications to extreme values

Recent group publications

Some key publications produced by the group:

• Eastoe, E.F. (2008) A hierarchical model for non-stationary multivariate extremes: a case study of surface-level ozone and NO_X data in the UK. To appear in Environmetrics.
  

• Heffernan, J.E., Tawn, J. A. and Zhang, Z. (2007) Asymptotically (in)dependent multivariate maxima of moving maxima processes. Extremes. 10, 57-83.
  

• Butler, A., Heffernan, J.E., Tawn, J.A. and Flather, R.A. (2007) Trend estimation in extremes of North Sea surges. Appl. Stats. 56, 395-414.
  

• Butler, A., Heffernan, J.E., Tawn, J.A., Flather, R.A. and Horsburgh, K. (2007) Extreme value analysis of decadal variations in storm surge elevations. Journal of Marine Systems 67, 189-200.
  

• Coles, S.G. and Tawn, J.A. (2005). Bayesian modelling extreme surges on the UK east coast. Phil. Trans. Roy. Soc. A: Mathematical, Physical and Engineering Sciences 363, 1387-1406.
  

• Coles, S.G. and Tawn, J.A. (2005). Seasonal effects of extreme surges. J. Stoch. Environ. Res. and Risk Assses. 19, 417-427.
  

• Heffernan, J.E. and Resnick, S.I. (2005). Hidden Regular Variation and the Rank Transform. Adv. Appl. Prob 37 (2), 393-414.
• Stephenson, A. and Tawn, J.A. (2005). Bayesian inference for extremes: accounting for the three extremal types. Extremes 7, 291-307.