###Novel estimation procedures for multivariate and spatial extreme value analysis
Project ID: 2228bd1161 (You will need this ID for your application)
Research Theme: Mathematical Sciences
UCL Lead department: Statistical Science
Lead Supervisor: Paul Northrop
Project Summary:
Extreme value analysis is the statistical study of unusually large or small values; often extrapolating to events not previously seen in a dataset by exploiting theoretically justified methodology. In an environmental setting, applications include modelling heavy rainfall, high winds, or low temperatures, with results aiming to mitigate the effect of future extreme events.
In multivariate and spatial settings, the aim is to study extreme behaviour simultaneously across different variables, or for one variable across multiple locations. This is important since the effect of such extreme events can be even more severe than for one variable individually. Extremes of these variables may tend to occur simultaneously, exhibiting extremal dependence. There are various frameworks available to capture extremal dependence in these settings. However, separate inference under these individual frameworks can lead to contradictory results, since consistent conclusions about the extremal dependence behaviour are not guaranteed.
Recent theoretical developments have found links between some different representations of extremal dependence. This involves taking a geometric approach and considering the limiting boundary shape of a suitably scaled sample cloud. Recent work by Simpson and Tawn (2022) exploits these theoretical results for inferential purposes but is limited to the bivariate case; extensions of this approach to allow for higher dimensional inference in multivariate and spatial settings are the focus of this PhD project.
The student will study the mathematical theory behind extreme value analysis and work on developing their own inferential approaches to tackle the lack of consistency across the extremal dependence frameworks. A student with a strong mathematical background, good programming skills, and a keen interest in developing novel statistical methodology would be ideally suited to this project.
Simpson, E. S. and Tawn, J. A. (2022). Estimating the limiting shape of bivariate scaled sample clouds for self-consistent inference of extremal dependence properties. arXiv:2207.02626.