Flexible random scale-mixture models provide a framework for capturing a broad range of extremal dependence structures. However, likelihood-based inference under the peaks-over-threshold setting is often computationally infeasible, due to the censored likelihood requiring repeated evaluation of high-dimensional Gaussian distribution functions. We propose a multiplicative log-Laplace nugget that yields conditional independence in the censored likelihood, resulting in a joint likelihood function that is the product of univariate densities which are available in closed form. This eliminates multivariate Gaussian distribution function evaluations and thereby enables inference for threshold exceedances in high dimensions, which represents a major shift for spatial extremes modelling as the total computational cost is now primarily driven by standard spatial statistics operations. We further show that a broad class of scale-mixture processes augmented with the proposed nugget preserves the extremal dependence structure of the underlying smooth process. The proposed methodology is illustrated through simulation studies and an application to precipitation extremes.

翻译：灵活的随机尺度混合模型为捕获广泛的极值依赖结构提供了框架。然而，在峰值超过阈值设定下，基于似然的推断通常计算上不可行，因为删失似然需要重复评估高维高斯分布函数。我们提出了一种乘法型 Log-Laplace Nugget，它在删失似然中产生条件独立性，从而得到联合似然函数为闭式单变量密度的乘积。这消除了多元高斯分布函数的评估，进而能够对高维度下的阈值超越进行推断——这对空间极值建模而言是一个重大转变，因为总计算成本现在主要由标准空间统计操作决定。我们进一步证明，用所提出的 Nugget 增强的广泛尺度混合过程类能保留底层光滑过程的极值依赖结构。通过模拟研究和对降水极值的应用示例，对所提出的方法进行了验证。