Abstract–Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity of repeatedly evaluating the multivariate Gaussian distribution function. In this work, we attempt to achieve truly high-dimensional inference for extremes of spatial processes, while retaining the desirable flexibility in the tail dependence structure, by modifying an established class of models based on scale mixtures Gaussian processes. We show that the desired extremal dependence properties from the original models are preserved under the modification, and demonstrate that the corresponding Bayesian hierarchical model does not involve the expensive computation of the multivariate Gaussian distribution function. We fit our model to exceedances of a high threshold, and perform coverage analyses and cross-model checks to validate its ability to capture different types of tail characteristics. We use a standard adaptive Metropolis algorithm for model fitting, and further accelerate the computation via parallelization and Rcpp. Lastly, we apply the model to a dataset of a fire threat index on the Great Plains region of the United States, which is vulnerable to massively destructive wildfires. We find that the joint tail of the fire threat index exhibits a decaying dependence structure that cannot be captured by limiting extreme value models. Supplementary materials for this article are available online.

摘要-最近文献中出现了允许尾部依赖类别之间转换的灵活空间模型。然而，由于需要重复评估多元高斯分布函数，即使在中等维度上，这些模型的推断在计算上也是令人望而却步的。在这项工作中，我们试图通过修改基于尺度混合高斯过程的已建立模型类，实现对空间过程极端情况的真正高维推理，同时在尾部依赖结构中保持理想的灵活性。我们表明，在修改后保留了原始模型所需的极值依赖属性，并证明相应的贝叶斯层次模型不涉及多元高斯分布函数的昂贵计算。我们将我们的模型拟合到超出高阈值的情况，并执行覆盖分析和跨模型检查以验证其捕获不同类型尾部特征的能力。我们使用标准的自适应 Metropolis 算法进行模型拟合，并通过并行化和 Rcpp 进一步加速计算。最后，我们将该模型应用于美国大平原地区的火灾威胁指数数据集，该地区容易受到大规模破坏性野火的影响。我们发现火灾威胁指数的联合尾部表现出一种衰减的依赖结构，不能通过极限极值模型来捕捉。