In this work, we develop a constructive modeling framework for extreme threshold exceedances in repeated observations of spatial fields, based on general product mixtures of random fields possessing light or heavy-tailed margins and various spatial dependence characteristics, which are suitably designed to provide high flexibility in the tail and at sub-asymptotic levels. Our proposed model is akin to a recently proposed Gamma-Gamma model using a ratio of processes with Gamma marginal distributions, but it possesses a higher degree of flexibility in its joint tail structure, capturing strong dependence more easily. We focus on constructions with the following three product factors, whose different roles ensure their statistical identifiability: a heavy-tailed spatially-dependent field, a lighter-tailed spatially-constant field, and another lighter-tailed spatially-independent field. Thanks to the model's hierarchical formulation, inference may be conveniently performed based on Markov chain Monte Carlo methods. We leverage the Metropolis adjusted Langevin algorithm (MALA) with random block proposals for latent variables, as well as the stochastic gradient Langevin dynamics (SGLD) algorithm for hyperparameters, in order to fit our proposed model very efficiently in relatively high spatio-temporal dimensions, while simultaneously censoring non-threshold exceedances and performing spatial prediction at multiple sites. The censoring mechanism is applied to the spatially independent component, such that only univariate cumulative distribution functions have to be evaluated. We explore the theoretical properties of the novel model, and illustrate the proposed methodology by simulation and application to daily precipitation data from North-Eastern Spain measured at about 100 stations over the period 2011-2020.
翻译:在这项工作中,我们根据拥有轻或重尾边距和各种空间依赖性特点的随机字段一般产品混合物,为反复观测空间字段中的极端阈值超值制定了一个建设性的建模框架,其基础是拥有轻或重尾边距和各种空间依赖性特点的随机字段的一般产品混合物,这些混合物设计得当,以便在尾部和亚防线层面提供高度的灵活性。我们提议的模型类似于最近提出的伽马-伽马模型,使用伽马边边际分布的流程比方,但它在联合尾部结构中具有更高程度的灵活性,更容易获得很强的依赖性。我们侧重于建筑中以下三个产品因素,其不同的作用确保其统计可识别性:一个高度快速的模拟空间依赖性字段、一个较轻的经空局宽的空局宽度字段和另一个较轻的地空间依赖性字段。由于模型的排列方式,根据Markov 链 Monte Caro方法,我们可能很方便地进行了推算。我们利用Metopolis调整过的朗埃文算法(MALA),只有随机的可变数组建议,以及用于潜在变数度的新版度应用的可测度变数度可变数度模型,以及用于可测度可测度的可测度可测度可测度可测度的轨道,在相对的轨道上可测度可测度可测度可测度的轨道的轨道的轨值,而可测度可测度可测量度可测度可测度可测量度的轨道,在SAL-直位度可测量度可达性轨道,在SAL-直径度可达度可达性轨道上,在Sir-直径度轨道上进行中,在SALDLDLDLD-直径的轨道上进行,在相对可达性轨道上,在SALDLD-直达性轨道上,在SAL-直达性轨道上,在SAL-直达性轨道上,在SAL-直达度上可达度可达度上可达度上可达度上可达度可达度可达性可达性可达性可达度可达度上可达度可达度上可达度可达度可达度可达度上可达度上,在SAL-直径