The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often suggests that such asymptotic models are too rigidly constrained, and that they do not adequately capture the frequent situation where more severe events tend to be spatially more localized. In other words, these asymptotic models have a strong tail dependence that persists at increasingly high levels, while data usually suggest that it should weaken instead. Another well-known limitation of classical spatial extremes models is that they are either computationally prohibitive to fit in high dimensions, or they need to be fitted using less efficient techniques. In this review paper, we describe recent progress in the modeling and inference for spatial extremes, focusing on new models that have more flexible tail structures that can bridge asymptotic dependence classes, and that are more easily amenable to likelihood-based inference for large datasets. In particular, we discuss various types of random scale constructions, as well as the conditional spatial extremes model, which have recently been getting increasing attention within the statistics of extremes community. We illustrate some of these new spatial models on two different environmental applications.
Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives
Department of Statistics and Data Science（统计与数据科学系）；Machine Learning Department（机器学习系）；Carnegie Mellon University（卡内基梅隆大学）；Statistics and Data Science Center（统计与数据科学中心）；Massachusetts Institute of Technology（麻省理工学院）
Spatial Extremes at Scale: A Case Study of Surface Skin Temperature and Heat Risk in the United States
George Mason University（乔治梅森大学）；University of Arkansas（阿肯色大学）；University of Edinburgh（爱丁堡大学）；University College London（伦敦大学学院）；University of Missouri（密苏里大学）
