Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial extreme value theory based on the conditional multivariate extreme value model, whereby the limit theory is formed through conditioning upon the value at a particular site being extreme. The ensuing methodology allows for a flexible class of dependence structures, as well as models that can be fitted in high dimensions. To overcome issues of conditioning on a single site, we suggest a joint inference scheme based on all observation locations, and implement an importance sampling algorithm to provide spatial realizations and estimates of quantities conditioning upon the process being extreme at any of one of an arbitrary set of locations. The modelling approach is applied to Australian summer temperature extremes, permitting assessment of the spatial extent of high temperature events over the continent.

当前可用的空间极端模型要么受到它们可以捕获的依赖结构的不灵活性，要么缺乏对高维的可扩展性，要么在大多数情况下两者兼而有之。我们提出了一种基于条件多元极值模型的空间极值理论方法，其中极限理论是通过以特定位置的极端值为条件来形成的。随后的方法允许一类灵活的依赖结构，以及可以在高维度上拟合的模型。为了克服单个站点的条件问题，我们建议基于所有观察位置的联合推理方案，并实施重要性采样算法，以提供空间实现和数量估计，条件是过程在任意一组位置中的任何一个位置处于极端状态。该建模方法适用于澳大利亚夏季极端温度，允许评估大陆上高温事件的空间范围。