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，例如重大发生的时间点或感兴趣的对象的空间位置。用统计术语，此类数据代表点过程。该研究项目的目的是研究跨多个点过程的相互作用集，引入了这些相互作用的新型统计估计方法，特别关注生态学最前沿的应用方法。在生态环境中，建模多个点过程之间的相互作用尤其重要。了解一个生态系统需要模型，即多种物种的发生如何在空间上，可能在几个时间实例上相互作用。现代数据集的大小通常涉及多个空间尺度的现代数据集的大小（通常涉及可观的物种数量和类型，但许多最重要的物种都非常罕见的地方，这些数据集的大小通常涉及物种数量和类型，这一大小通常涉及物种的数量和类型。迫切需要在该领域的新方法，并将通过两个工作包进行开发：首先，在高维环境中，估计了许多非常异构相互作用的量度；其次，引入了基于规模的大型相互作用的分析。这些方法将从时间序列分析（PI当前奖学金的主题）以及随机矩阵理论中最新发展的十年中适应和扩展工具，适应了相互作用的度量。因此，该项目属于统计和学科研究的职责。两者都在当前的EPSRC奖学金优先领域强调。该项目的结果将直接影响特定的生态推理应用（例如生态的Barro Colorado Island树数据集）和多点过程的理论，以及更普遍的高维统计数据分析的重要当代领域。