Addressing modern challenges in spatial extreme value modelling

极值分析是处理罕见事件的统计学的一个分支，即异常大或小的值。它的作用是了解这些事件的概率规律，并提供合适的统计模型来描述真实的数据集的极端行为。在实践中，极值方法主要用作风险评估工具，允许外推比已经观察到的更极端（因此更具灾难性）的事件的结果。这个博士项目将极值理论与空间统计相结合，研究时空环境数据集的极端行为。我们正在研究气象局哈德利中心制作的区域气候模型预测，作为英国气候预测2018（UKCP18）项目的一部分。这些数据提供了英国从1980年到2080年的气候变化信息，缩小到高分辨率（12公里），有助于适应气候变化。特别是，我们的数据包括每日最高温度预测为英国，模拟下的高排放情景（RCP 8.5）。上述数据的初步分析表明，所观察到的数据的空间依赖性的时间非平稳性。大部分现有的方法来分析这样的时空数据集只能容纳静态随时间的依赖结构。然而，由于气候变化，我们可能会看到越来越多的环境数据集在其依赖结构中表现出这种非平稳特性。因此，我们在这个项目中的目标是从条件空间极值框架扩展现有的方法，以适应时间非平稳数据集的分析。如果成功完成这个方法学的努力，我希望在我的研究期间可能发生的任何后续项目中，我将设法探索/解决尽可能多的空间/时空极值统计领域的方法挑战。

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.