Statistical Theory and Methods to Transform our Understanding of Network Data

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The principal subject of this research is the study of networks as statistical data objects. Networks are fundamental to our modern world: they appear throughout science and society, and continue to grow in size, complexity and importance. Whenever we observe entities and relationships between them, we effectively define a network of some sort. As structural objects composed of nodes and links, networks play a strong and well defined role across mathematics, science and engineering. As statistical objects made up of collections of measurements, however, network datasets require significant advances to be made in mathematical knowledge if we are to achieve fundamental understanding.The crux of the problem, and the essence of the approach to be undertaken in this research, lies in finding the right balance between complexity and parsimony. Currently, the network models that we understand fully from a mathematical viewpoint are too simple to accurately describe modern data. At the same time, models sufficiently rich to provide accurate descriptions are presently beyond our mathematical comprehension, meaning that we cannot use them to draw sound and repeatable conclusions from data. This fundamental lack of understanding slows scientific progress and affects every single economic, social or other policy decision that relies on the analysis of network data.The main objectives of this research are therefore twofold: first, to develop the new statistical theory needed to view and interpret networks properly as data objects; and second, to transform this theory into new statistical methods that will allow us to model and draw inferences from network data in the real world. These objectives reflect the fact that network modelling and inference is an area of significant national importance. It spans the many diverse fields and contexts where inferences must be drawn and substantiated based on measurements of entities and the relationships or interactions between them.As networks grow in size and complexity, our ability to analyse them using modern statistical methods is at severe risk of failing to keep pace. Recent theoretical breakthroughs by the fellowship applicant have provided initial headway towards answering longstanding open questions in this area, creating an immediate and direct opportunity to close the fundamental and growing gap between our need to understand network data and our ability to do so. Doing so will provide the UK with a unique capability to lead research developments at the international forefront of this area.This research will deliver a core set of statistical fundamentals that provide both the strong theoretical underpinnings and the practical tools required to revolutionise network modelling and inference. The work will be carried out in the Department of Statistical Science, University College London, and will involve collaborations with subject matter experts drawn both from within the University and from across the academic community and industry partners.The methods developed will be applied to a range of important practical problems, so that they may be assessed, refined and improved while under development. This will provide a direct pathway to impact and establish a tight coupling between the mathematical advancements to be achieved and the important practical problems that these advancements will benefit. It will also open up new mathematical connections with other disciplines where networks play a key role, such as the life sciences, and lead directly to new techniques that impact research users across a range of important practical applications that directly affect the health, security and economic competitiveness of the UK populace.