Project Title: Extreme value models for climate risk estimation
The University of Exeter’s Department of Mathematics and Statistics is inviting applications for a fully-funded PhD studentship to commence on or around 25 September 2023. For eligible students the studentship will cover Home tuition fees plus an annual tax-free stipend of at least £17,668 for 3.5 years full-time, or pro rata for part-time study. The student would be based in the Department of Mathematics and Statistics in the Faculty of Environment, Science and Economy at the Streatham Campus in Exeter.
Project Description:
Statistical models developed with extreme value theory as a basis allow us to use established mathematics to make probabilistic risk estimates, such as for 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. Since they can cause considerable damage, it is fortunate that extreme events are by definition rare. Unfortunately, from a statistical perspective, this means data quantifying such events are usually scarce. This project aims to develop models that better use data to improve our understanding of rare weather events
Statistical modelling of extremes has seen a step change in methodology for representing spatial processes over the last 20 years; see, e.g., Davison and Gholamrezaee (2012), for a review. This is statistically important because with these models we can pool data from multiple locations and partially compensate for data scarcity, when compared to considering each location on its own. Further recent developments, such as Engelke et al. (2018), bring models for extreme events that can extrapolate to higher resolutions than the resolution of the data we have. Advances in resolution of data from numerical weather simulation models may yet be insufficient to give accurate weather risk estimates for some phenomena, but we can now consider using these data with extreme value models to make higher-resolution prediction with the potential to significantly improve risk estimation.
This project will develop a novel statistical framework that incorporates extreme value theory and geostatistics for modelling processes at the higher-resolutions necessary for risk estimation (Youngman, 2019). This will require incorporating efficiencies to make tractable the modelling of Big Data, such as gridded environmental data covering large regions. Complex dependencies must be expected in such data, which will be captured through deep Gaussian processes and generalised additive models (Youngman, 2020). This project will combine developing statistical models with producing user-friendly software for fitting the models. 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.
References
- Davison, A. C. and Gholamrezaee, M. M. (2012). Geostatistics of extremes. Proc. R. Soc. A, DOI: 10.1098/rspa.2011.0412
- Engelke, S., De Fondeville, R., and Oesting, M. (2018). Extremal behaviour of aggregated data with an application to downscaling. Biometrika, DOI: 10.1093/biomet/asy052
- Youngman, B. D. (2019). Generalized additive models for exceedances of high thresholds with an application to return level estimation for U.S. wind gusts. J. Am. Stat. Assoc. DOI: 10.1080/01621459.2018.1529596
- Youngman, B. D. (2020). Flexible models for nonstationary dependence: Methodology and examples. arXiv. DOI: 10.48550/ARXIV.2001.06642
For project further details, contact Dr Ben Youngman on b.youngman@exeter.ac.uk. For further application details, contact pgrenquiries@exeter.ac.uk.
