Fitting max-stable processes to high-dimensional data

In 2019-2020 a large part of Australia was facing major bushfires. During this “black summer” at least 34 people perished in the flames and about 30 million hectares and 6000 building were burned. The 2021-2022 summer in Australia has been marred by intense heatwaves and bushfires in the west, and devastating floods in the east. Such extreme events seem to appear with increasing frequency, creating an urgent need to better understand the behaviour of extreme environmental phenomena. Max-stable processes are a widely popular tool to model spatial extreme events with several flexible models available in the literature. For inference on max-stable models, exact likelihood estimation becomes quickly computationally intractable as the number of spatial locations grows, limiting their applicability to large study regions or fine grids. In this talk, we introduce two methodologies based on composite likelihoods, to circumvent this issue. First, we assume the occurrence times of maxima available in order to incorporate the Stephenson-Tawn concept into the composite likelihood framework. Second, we propose to aggregate the information between locations into histograms and to derive a composite likelihood variation for these summaries. The significant improvements in performance of each estimation procedures is established through simulation studies and illustrated on two temperature datasets from Australia.

Mar 12, 2022