We develop a methodology for modelling and simulating high-dimensional spatial precipitation extremes, using a combination of the spatial conditional extremes model, latent Gaussian models and integrated nested Laplace approximations (INLA). The spatial conditional extremes model requires data with Laplace marginal distributions, but precipitation distributions contain point masses at zero that complicate necessary standardisation procedures. We propose to model conditional extremes of nonzero precipitation only, while separately modelling precipitation occurrences. The two models are then combined to create a complete model for extreme precipitation. Nonzero precipitation marginals are modelled using a combination of latent Gaussian models with gamma and generalised Pareto likelihoods. Four different models for precipitation occurrence are investigated. New empirical diagnostics and parametric models are developed for describing components of the spatial conditional extremes model. We apply our framework to simulate spatial precipitation extremes over a water catchment in Central Norway, using high-density radar data. Inference on a 6000-dimensional data set is performed within hours, and the simulated data capture the main trends of the observed data well.

翻译：我们提出了一种结合空间条件极值模型、潜高斯模型与积分嵌套拉普拉斯近似的方法，用于建模和模拟高维空间极端降水数据。空间条件极值模型要求数据服从拉普拉斯边际分布，但降水分布中包含零点质量，这使必要的标准化过程变得复杂。我们建议仅对非零降水量的条件极值进行建模，同时单独对降水发生事件进行建模。通过将两个模型结合，构建了完整的极端降水模型。非零降水的边际分布采用伽马分布与广义帕累托似然的潜高斯模型进行建模。研究了四种不同的降水发生模型。针对空间条件极值模型的组成部分，开发了新的经验诊断方法与参数模型。我们将该框架应用于挪威中部某流域的高密度雷达数据，模拟空间极端降水。对6000维数据集的推理可在数小时内完成，且模拟数据较好地捕捉了观测数据的主要趋势。