Modeling nonstationarity that often prevails in extremal dependence of spatial data can be challenging, and typically requires bespoke or complex spatial models that are difficult to estimate. Inference for stationary and isotropic models is considerably easier, but the assumptions that underpin these models are rarely met by data observed over large or topographically complex domains. A possible approach for accommodating nonstationarity in a spatial model is to warp the spatial domain to a latent space where stationarity and isotropy can be reasonably assumed. Although this approach is very flexible, estimating the warping function can be computationally expensive, and the transformation is not always guaranteed to be bijective, which may lead to physically unrealistic transformations when the domain folds onto itself. We overcome these challenges by developing deep compositional spatial models to capture nonstationarity in extremal dependence. Specifically, we focus on modeling high threshold exceedances of process functionals by leveraging efficient inference methods for limiting r-Pareto processes. A detailed high-dimensional simulation study demonstrates the superior performance of our model in estimating the warped space. We illustrate our method by modeling UK precipitation extremes and show that we can efficiently estimate the extremal dependence structure of data observed at thousands of locations.

翻译：建模空间数据极端依赖性中常见的非平稳性是一项挑战，通常需要定制或复杂的空间模型，且这些模型难以估计。平稳和各向同性模型的推断相对容易，但其假设条件很少能被在大范围或地形复杂区域观测到的数据所满足。处理空间模型中非平稳性的一种可行方法是将空间域扭曲到一个可合理假设平稳性和各向同性的潜在空间。尽管该方法非常灵活，但估计扭曲函数的计算成本较高，且变换并不总能保证双射性，这可能导致域自折叠时出现物理上不合理的变换。我们通过开发深层组合空间模型来捕捉极端依赖性中的非平稳性，从而克服了这些挑战。具体而言，我们专注于通过利用极限r-Pareto过程的高效推断方法对过程泛函的高阈值超越事件进行建模。一项详细的高维模拟研究证明了我们的模型在估计扭曲空间方面的优越性能。我们通过对英国降水极值的建模展示了该方法，结果表明我们能高效估计数千个位置观测数据的极端依赖性结构。