Spatial modelling of extreme values allows studying the risk of joint occurrence of extreme events at different locations and is of significant interest in climatic and other environmental sciences. A popular class of dependence models for spatial extremes is that of random location-scale mixtures, in which a spatial "baseline" process is multiplied or shifted by a random variable, potentially altering its extremal dependence behaviour. Gaussian location-scale mixtures retain benefits of their Gaussian baseline processes while overcoming some of their limitations, such as symmetry, light tails and weak tail dependence. We review properties of Gaussian location-scale mixtures and develop novel constructions with interesting features, together with a general algorithm for conditional simulation from these models. We leverage their flexibility to propose extended extreme-value models, that allow for appropriately modelling not only the tails but also the bulk of the data. This is important in many applications and avoids the need to explicitly select the events considered as extreme. We propose new solutions for likelihood inference in parametric models of Gaussian location-scale mixtures, in order to avoid the numerical bottleneck given by the latent location and scale variables that can lead to high computational cost of standard likelihood evaluations. The effectiveness of the models and of the inference methods is confirmed with simulated data examples, and we present an application to wildfire-related weather variables in Portugal. Although not detailed here, the approaches would also be straightforward to use for modelling multivariate (non spatial) data.

翻译：空间极值建模能够研究不同位置极端事件联合发生的风险，在气候学及其他环境科学领域具有重要价值。随机位置-尺度混合模型是空间极值依赖建模的主流方法之一，该方法通过对空间"基线"过程进行随机变量的乘法或平移变换，从而可能改变其极值依赖特性。高斯位置-尺度混合模型在保留高斯基线过程优势的同时，克服了其对称性、轻尾分布和弱尾部依赖等局限性。本文系统综述了高斯位置-尺度混合模型的性质，构建了具有新颖特征的新型模型结构，并提出了适用于此类模型的条件模拟通用算法。我们利用其灵活性构建了扩展极值模型，该模型不仅能准确刻画数据尾部特征，还能有效拟合数据主体部分。这在众多应用场景中至关重要，且无需显式选择被视为极端的事件。针对高斯位置-尺度混合参数模型，我们提出了新的似然推断解决方案，以规避由潜位置变量和尺度变量导致的数值计算瓶颈——该瓶颈常使标准似然评估产生高昂计算成本。通过模拟数据实验验证了模型及推断方法的有效性，并以葡萄牙野火相关气象变量为例进行了实证分析。需要说明的是，尽管未详细展开，该方法同样适用于多元（非空间）数据的建模场景。