Addressing modern challenges in spatial extreme value modelling

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PhD Project Description:Extreme value analysis is a branch of statistics dealing with rare events; that is, unusually large or small values. Its role is to understand the probability laws governing such events and to provide suitable statistical models to describe the extremal behaviour of real datasets. In practice, extreme value methods are primarily used as risk assessment tools, allowing for extrapolation of results for more extreme (and therefore more catastrophic) events than the ones already observed.This PhD project combines extreme value theory with spatial statistics to study the extremal behaviour of a spatiotemporal environmental dataset. We are looking at regional climate model projections produced by the Met Office Hadley Centre as part of the UK Climate Projection 2018 (UKCP18) project. The data provides information on changes in climate for the UK from 1980 until 2080, downscaled to a high resolution (12km), helping to inform adaptation to a changing climate. In particular, our data comprise daily maximum temperature projections for the UK, simulated under a high emissions scenario (RCP8.5).Preliminary analysis of the aforementioned data has suggested temporal non-stationarities in the observed spatial dependence of the data. Much of the existing methodology for analysing such spatiotemporal datasets can accommodate only stationary-over-time dependence structures. However, because of climate change, it is possible that we will see more and more environmental datasets showcasing such non-stationary characteristics in their dependence structures. Therefore, our goal in this project is to extend existing methodology from the conditional spatial extremes framework to accommodate the analysis of temporally non-stationary datasets as well.Provided the successful completion of this methodological endeavour, my hope is that in any subsequent projects that may occur in the duration of my research studies, I will manage to explore/address as many methodological challenges as possible in the field of spatial/spatiotemporal extreme-value statistics.