University of Exeter PhD Studentships in Mathematics

  • Phd
  • Tuition fees + £15,609 p.a.
  • 10 January 2022

Project Description:

Statistical models developed with extreme value theory as a basis allow us to use established mathematics to make probabilistic estimates about rare weather events. For example, we can take data and estimate 1-in-100 year events, and their uncertainty. This can even be done with fewer than 100 years worth of data. Fortunately, since they can cause considerable damage, such events are by definition rare. Unfortunately, from a statistical perspective, this means data quantifying them are inevitably scarce. This project aims to develop models that better use data so that we can make more accurate our understanding of extreme weather events.

Statistical modelling of extremes has recently seen a step change in methodology for representing spatial processes; see, e.g., Davison and Gholamrezaee (2012), for a review. The statistical importance of this is that we can pool data from multiple locations, which can partially compensate for data scarcity, when compared to considering each location on its own. Further recent developments, such as Engelke et al. (2018), allow us to model extreme events represented by finite-resolution data. This is important because numerical weather simulation models are a valuable source of such data and have now reached resolutions capable of capturing extreme meteorological phenomena that previously were previously unreliably modelled. If we can coherently link the statistical and numerical developments, we can improve risk estimation of extreme weather events. However, if we can also reliably incorporate climate projections and their uncertainty, then we can further - and perhaps dramatically - improve our understanding of future extreme weather risk.

Linking statistical and numerical developments will need a novel statistical framework that incorporates extreme value theory and spatial statistics; it must be capable of handling large quantities of aggregated data, avoiding excessive computational cost, and must explicitly recognise the discrepancies that are inevitable in model-generated data. Conventional approaches won’t suffice: they’re only feasible for small amounts of high-resolution data, which limits their applicability to very small regions, and they lack the robustness to readily incorporate climate projection uncertainty. However, we can now draw on developments for deep Gaussian processes and generalised additive models to build a framework that can applied in a valuable way to many more - and potentially all - extreme weather phenomena. This project will first develop such a framework, which will then be translated to efficient, user-friendly software. The proposed framework could benefit a considerable number of end-users, and ultimately bring new, quantitative understanding of risk for a variety of types of extreme weather.

Eligibility

This studentship is open to UK and Irish nationals, who if successful in their application will receive a full studentship including payment of university tuition fees at the home fees rate.

Applicants for this studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology.

Degree in mathematics and/or statistics required.

If English is not your first language you will need to have achieved at least 6.0 in IELTS and no less than 6.0 in any section by the start of the project. Alternative tests may be acceptable (see http://www.exeter.ac.uk/postgraduate/apply/english/).

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Benefits

Home tuition fees plus an annual tax-free stipend of at least £15,609 for 3.5 years full-time, or pro rata for part-time study.

Application

Necessary documents:

  • CV
  • Letter of application (outlining your academic interests, prior project work experience and reasons for
      wishing to undertake the project).
  • Transcript(s) giving full details of subjects studied and grades/marks obtained (this should be an
       interim transcript if you are still studying)
  • Two references from referees familiar with your academic work. If your referees prefer, they can email
       the reference direct to pgrenquiries@exeter.ac.uk quoting the studentship reference number.
  • If you are not a national of a majority English-speaking country you will need to submit evidence of your proficiency in English.  Please see the entry requirements information above.
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