Characterizing Interactions Across Large-Scale Point Process Populations

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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.