Characterizing Interactions Across Large-Scale Point Process Populations

许多生态和其他科学数据集采取记录事件的形式，例如重大事件的时间点或感兴趣对象的空间位置。在统计学术语中，这些数据代表点过程。该研究项目的目的是研究多点过程之间的相互作用，为这些相互作用引入新的统计估计方法，特别关注生态学前沿应用的方法。在生态环境中，模拟多组点过程之间的相互作用尤为重要。理解一个生态系统需要多个物种如何在空间上相互作用的模型，可能跨越几个时间实例。现代数据集的规模加剧了目前对这一领域理论认识的缺乏，这些数据集通常涉及多个空间尺度上可观的物种数量和类型，但其中许多最重要的物种非常罕见。新的方法在这一领域是迫切需要的，并将通过两个工作包开发：第一，在高维设置，估计非常异构的相互作用的许多措施;第二，引入基于规模的分析大套的相互作用。这些方法将适应和扩展工具从时间序列分析-PI的当前奖学金的主题-和随机矩阵理论的最近十年的发展，适应相互作用的措施的集合。因此，该项目福尔斯属于统计和学科内研究的范围;这两个领域都是目前EPSRC研究金优先领域的重点。该项目的成果将直接影响特定的生态推理应用（如生态巴罗科罗拉多岛树数据集）和多点过程理论，以及更普遍的高维统计数据分析的重要当代领域。

Many ecological and other scientific datasets take the form of recorded events, such as time points of significant occurrences, or spatial locations of objects of interest. In statistical terms, such data represent point processes. The purpose of this research project is to study sets of interactions across multiple point processes, introducing novel statistical estimation methods for these interactions, with a specific focus on methods for applications at the forefront of ecology. In ecological settings it is particularly important to model the interactions between multiple sets of point processes. Understanding an ecosystem requires models of how occurrences of multiple species interact spatially, potentially across several time instances. The current lack of theoretical understanding in this area is exacerbated by the sizes of modern datasets, which typically involve appreciable numbers and types of species, across multiple spatial scales, but also where many of the most important species are quite rare. Novel methodology in this area is urgently needed, and will be developed via two work packages: first, in the high-dimensional setting, estimating many measures of very heterogeneous interactions; and second, introducing scale-based analysis of large sets of interactions. These approaches will adapt and extend tools from time series analysis - the subject of the PI's current fellowship - and the decade of recent developments in random matrix theory, adapted to collections of measures of interactions. The project thus falls in the remit of both statistics and intradisciplinary research; both highlighted under current EPSRC fellowship priority areas. The outcomes of the project will directly impact specific ecological inference applications (such as the ecological Barro Colorado Island tree data set) and the theory of multiple point processes, as well as more generally the important contemporary area of high-dimensional statistical data analysis.