Estimation of spatio-temporal extremes via generative neural networks

As the frequency of extreme weather events rises, it becomes increasingly crucial to understand and detect them at the earliest opportunity. Statistical models provide a way to enhance their interpretability and offer insights into the connections between extreme events. Since geophysical data is often coupled across both space and time this poses challenges for modeling, often leading to highly complex statistical models. For spatial data, such as precipitation, a common way to describe and analyze extremes are max-stable processes, which arise as the unique limit of pointwise maxima of random fields. These processes are an essential tool in analyzing spatial extremes (Davison et al., 2012), as they allow for flexible modeling of the underlying dependence structure. However, when it comes to modeling these extremes, usually only a few observations are available, even less so as the underlying process is usually changing across time. For that reason traditional statistical methods often fail to identify parameters correctly, particularly as these models are high dimensional and complex. Furthermore, estimating parameters becomes especially challenging when dealing with extreme values. Therefore, specifying a distribution rather than relying on point estimators can be beneficial for quantifying uncertainty.