时间演化和空间全局相关数据建模
Modeling Temporally Evolving and Spatially Globally Dependent Data
摘要：
在过去几十年中，从遥感网络到气候模型集合，具有全球性和随时间变化的数据集的可用性空前增加。本文提供了一个时空过程的统计建模技术的视图，其中空间是代表我们的星球的球体。特别是，我们（a）二阶为基础的，和（b）实际的方法来模拟时间演变的全球过程之间的区别。前者是基于一类时空协方差函数的规范，空间是二维球面。后者基于对时空过程动力学的明确描述，即，通过将其演变指定为具有附加的空间相关噪声的其过去历史的函数。我们特别关注方法（a），文献很少。本文给出了定义在球面上的随机场的时空协方差函数的新模型。实用的方法，（b），也进行了讨论，特别强调直接建立在球体上的模型，而不投影的球面坐标在平面上。我们提出了一个案例研究，重点分析了2015年赤道亚洲野火的空气污染，这一事件被列为今年最严重的环境灾难。本文最后列出了该领域的主要理论和应用研究问题，我们希望统计界在未来十年内参与其中。
英文摘要：
The last decades have seen an unprecedented increase in the availability of data sets that are inherently global and temporally evolving, from remotely sensed networks to climate model ensembles. This paper provides a view of statistical modeling techniques for space-time processes, where space is the sphere representing our planet. In particular, we make a distintion between (a) second order-based, and (b) practical approaches to model temporally evolving global processes. The former are based on the specification of a class of space-time covariance functions, with space being the two-dimensional sphere. The latter are based on explicit description of the dynamics of the space-time process, i.e., by specifying its evolution as a function of its past history with added spatially dependent noise. We especially focus on approach (a), where the literature has been sparse. We provide new models of space-time covariance functions for random fields defined on spheres cross time. Practical approaches, (b), are also discussed, with special emphasis on models built directly on the sphere, without projecting the spherical coordinate on the plane. We present a case study focused on the analysis of air pollution from the 2015 wildfires in Equatorial Asia, an event which was classified as the year's worst environmental disaster. The paper finishes with a list of the main theoretical and applied research problems in the area, where we expect the statistical community to engage over the next decade.
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