Spatio-temporal Point Process models on a global scale and their application to global lightning occurrences

随着最近的技术进步和网络连接的增加，在全球范围内收集了许多环境、生物和社会经济数据集。然而，目前的许多统计模型和方法并不适用于数据覆盖球体表面的环境应用。该项目的目标是在全球范围内开发空间和时空点过程模型。这项研究的动机是一项关于全球闪电发生的研究，以及气候变化对全球闪电发生模式的影响。这项研究将为科学家、政策制定者和公众提供有用的信息。所提出的模型将解决强度函数的空间不均匀性及其非平稳性，这两者对于环境应用都是必不可少的。在时空情况下，将研究能够表示复杂时空相互作用的随机强度函数的参数协方差模型，并将考虑考虑多个点模式之间的交叉依赖的单变量和多变量点模式。

With recent technological advances and increased network connectivity, many environmental, biological, and socio-economic datasets are collected on a global scale. However, many of the current statistical models and methods are not suitable for environmental applications where the data cover the surface of the sphere. The goal of this project is to develop spatial and spatio-temporal point process models on a global scale. The research is motivated by a study of global lightning occurrence, and the impact of climate change on global lightning occurrence patterns. The research will provide useful information for scientists, policy makers, and the general public. The proposed models will address the spatial inhomogeneity of the intensity functions as well as their nonstationarity, both of which are essential for environmental applications. In the spatio-temporal case, parametric covariance models for the stochastic intensity function that can represent complex spatio-temporal interactions will be studied, and univariate as well as multivariate point patterns that account for the cross-dependence between multiple point patterns will be considered.