Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize "data-level dependence'' in analysis of extreme events, we propose a mixture model that achieves flexible dependence properties and allows high-dimensional inference for extremes of spatial processes. We modify the popular random scale construction that multiplies a Gaussian random field by a single radial variable; we allow the radial variable to vary smoothly across space and add non-stationarity to the Gaussian process. As the level of extremeness increases, this single model exhibits both asymptotic independence at long ranges and either asymptotic dependence or independence at short ranges. We make joint inference on the dependence model and a marginal model using a copula approach within a Bayesian hierarchical model. Three different simulation scenarios show close to nominal frequentist coverage rates. Lastly, we apply the model to a dataset of extreme summertime precipitation over the central United States. We find that the joint tail of precipitation exhibits non-stationary dependence structure that cannot be captured by limiting extreme value models or current state-of-the-art sub-asymptotic models.

翻译：大空间域上的极端事件可能展现出高度异质化的尾相依特征，然而现有的大多数空间极值模型在整个空间域上仅能产生单一的相依类别。为了在极端事件分析中准确刻画"数据层面的相依性"，我们提出了一种混合模型，该模型能够实现灵活的相依特性，并允许对空间过程极值进行高维推断。我们改进了流行的随机尺度构造方法——该方法将高斯随机场乘以单一的径向变量；我们允许径向变量在空间上平滑变化，并为高斯过程添加了非平稳性。随着极端程度的增加，该单一模型在长距离上展现出渐近独立性，同时在短距离上展现出渐近相依性或渐近独立性。我们在贝叶斯层次模型中采用Copula方法，对相依模型与边缘模型进行联合推断。三种不同的模拟场景显示，其频率覆盖概率接近名义水平。最后，我们将该模型应用于美国中部地区极端夏季降水数据集。研究发现，降水的联合尾部呈现出非平稳的相依结构，这一结构无法被极限极值模型或当前最先进的亚渐近模型所捕捉。