降水资料的分层时空模拟及其应用
Hierarchical space-time modeling of exceedances with an application to rainfall data
摘要：
在环境应用中，时空极值的统计建模是理解原始事件数据中复杂依赖结构和为影响模型生成现实情景的关键。在这种情况下，高维数据，我们提出了一种新的分层模型定义在连续的空间和时间的高阈值的卷积，通过嵌入一个空间-时间伽马过程卷积的指数变量的速率，导致在空间和时间的渐近独立。其物理动机的各向异性依赖结构是基于几何对象根据速度矢量在时空中移动。我们证明了基于加权成对似然的推理是快速和准确的。我们的模型的有用性说明了从法国南部的研究区域，它显然提高了一个替代的删失高斯时空随机场模型的应用程序每小时的降水数据。虽然经典的极限模型阈值稳定的基础上，未能适当地捕捉相对较快的联合尾部衰减率之间的渐近依赖和经典的独立性，强有力的经验证据，从我们的应用程序和其他最近的案例研究，激励使用更现实的渐近独立模型，如我们的。
英文摘要：
The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of high-dimensional data, we propose a novel hierarchical model for high threshold exceedances defined over continuous space and time by embedding a space-time Gamma process convolution for the rate of an exponential variable, leading to asymptotic independence in space and time. Its physically motivated anisotropic dependence structure is based on geometric objects moving through space-time according to a velocity vector. We demonstrate that inference based on weighted pairwise likelihood is fast and accurate. The usefulness of our model is illustrated by an application to hourly precipitation data from a study region in Southern France, where it clearly improves on an alternative censored Gaussian space-time random field model. While classical limit models based on threshold-stability fail to appropriately capture relatively fast joint tail decay rates between asymptotic dependence and classical independence, strong empirical evidence from our application and other recent case studies motivates the use of more realistic asymptotic independence models such as ours.
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