Characterizing Interactions Across Large-Scale Point Process Populations

表征大规模点过程群体之间的交互

基本信息

批准号：
EP/L001519/1
负责人：
Sofia Olhede
金额：
$ 19.39万
依托单位：
University College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2013
资助国家：
英国
起止时间：
2013 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FL001519%2F1
关键词：
Characterizing Interactions Across Large Scale

项目摘要

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.

许多生态和其他科学数据集采用记录事件的形式，例如重大事件的时间点或感兴趣物体的空间位置。从统计学角度来说，这些数据代表点过程。该研究项目的目的是研究跨多点过程的相互作用集，为这些相互作用引入新颖的统计估计方法，特别关注生态学前沿的应用方法。在生态环境中，对多组点过程之间的相互作用进行建模尤为重要。了解生态系统需要模型来了解多个物种的出现如何在空间上相互作用，可能跨多个时间实例。现代数据集的规模加剧了当前对该领域理论理解的缺乏，这些数据集通常涉及跨多个空间尺度的相当数量和类型的物种，但许多最重要的物种也相当罕见。该领域迫切需要新的方法，并将通过两个工作包来开发：首先，在高维环境中，估计非常异构的相互作用的许多度量；其次，引入对大量交互的基于尺度的分析。这些方法将适应和扩展时间序列分析（PI当前研究金的主题）和随机矩阵理论最近十年发展的工具，适应相互作用测量的集合。因此，该项目属于统计学和跨学科研究的范围；两者均在当前 EPSRC 研究金优先领域中得到强调。该项目的成果将直接影响特定的生态推理应用（例如生态巴罗科罗拉多岛树木数据集）和多点过程理论，以及更广泛的当代高维统计数据分析的重要领域。