Dynamic networks occur in many fields of science, technology and medicine, as well as everyday life. Understanding their behaviour has important applications. For example, whether it is to uncover serious crime on the dark web, intrusions in a computer network, or hijacks at global internet scales, better network anomaly detection tools are desperately needed in cyber-security. Characterising the network structure of multiple EEG time series recorded at different locations in the brain is critical for understanding neurological disorders and therapeutics development. Modelling dynamic networks is of great interest in transport applications, such as for preventing accidents on highways and predicting the influence of bad weather on train networks. Systematically identifying, attributing, and preventing misinformation online requires realistic models of information flow in social networks. Whilst simple random networks theory is well-established in maths and computer science, the recent explosion of dynamic network data has exposed a large gap in our ability to process real-life networks. Classical network models have led to a body of beautiful mathematical theory, but do not always capture the rich structure and temporal dynamics seen in real data, nor are they geared to answer practitioners' typical questions, e.g. relating to forecasting, anomaly detection or data ethics issues. Our NeST programme will develop robust, principled, yet computationally feasible ways of modelling dynamically changing networks and the statistical processes on them. Some aspects of these problems, such as quantifying the influence of policy interventions on the spread of misinformation or disease, require advances in probability theory. Dynamic network data are also notoriously difficult to analyse. At a computational level, the datasets are often very large and/or only available "on the stream". At a statistical level, they often come with important collection biases and missing data. Often, even understanding the data and how they may relate to the analysis goal can be challenging. Therefore, to tackle these research questions in a systematic way we need to bring probabilists, statisticians and application domain experts together. NeST's six-year programme will see probabilists and statisticians with theoretical, computational, machine learning and data science expertise, collaborate across six world-class institutes to conduct leading and impactful research. In different overlapping groups, we will tackle questions such as: How do we model data to capture the complex features and dynamics we observe in practice? How should we conduct exploratory data analysis or, to quote a famous statistician, "Looking at the data to see what it seems to say" (Tukey, 1977)? How can we forecast network data, or detect anomalies, changes, trends? To ground techniques in practice, our research will be informed and driven by challenges in many key scientific disciplines through frequent interaction with industrial & government partners in energy, cyber-security, the environment, finance, logistics, statistics, telecoms, transport, and biology. A valuable output of work will be high-quality, curated, dynamic network datasets from a broad range of application domains, which we will make publicly available in a repository for benchmarking, testing & reproducibility (responsible innovation), partly as a vehicle to foster new collaborations. We also have a strategy to disseminate knowledge through a diverse range of scientific publication routes, high-quality free software (e.g. R packages, Python notebooks accompanying data releases), conferences, patents and outreach activities. NeST will also carefully nurture and develop the next generation of highly-trained and research-active people in our area, which will contribute strongly to satisfying the high demand for such people in industry, government and academia.

The EPSRC Centre for Doctoral Training in Statistics and Machine Learning (StatML) will address the EPSRC research priority of the 'physical and mathematical sciences powerhouse' through an innovative cohort-based training program. StatML harnesses the combined strengths of Imperial and Oxford, two world-leading institutions in statistics and machine learning, in collaboration with a broad spectrum of industry partners, to nurture the next generation of leaders in this field. Our students will be at the forefront of advancing the core methodologies of data science and AI, crucial for unlocking the value inherent in data to benefit industry and society. They will be equipped with advanced research, technical, and practical skills, enabling them to make tangible real-world impacts. Our students will be ethical and responsible innovators, championing reproducible research and open science. Collaborating with students, charities and equality experts, StatML will also pioneer a comprehensive strategy to promote inclusivity, attract individuals from diverse backgrounds and eliminate biases. This will help diversify the UK's future statistics and machine learning workforce, essential for ensuring data science is used for public good. Data science and AI are now part of our everyday lives, transforming all sectors of the economy. To future-proof the UK's prosperity and security, it is essential to develop new methodology, specifically tailored to meet the big societal challenges of the future. The techniques underpinning such methods are founded in statistics and machine learning. Through close collaboration with a broad range of industry partners, our cohort-based training will support the UK in producing a critical mass of world-leading researchers with expertise in developing cutting-edge, impactful statistical and machine learning methodology and theory. It is well documented in government and learned society reports that the UK economy has an urgent need for these people. The significant level of industry support for our proposal also highlights the necessity of filling this gap in the UK data science ecosystem. StatML will learn from and build upon our previous successful experiences in cohort training of doctoral students (our existing StatML CDT funded in 2018, as well as other CDTs at Imperial and Oxford). Our students will continue to produce impactful, internationally leading research in statistics and machine learning (as evidenced by our students' impressive publication record and our world-leading research environment, as rated by the REF 2021 evaluation), while complementing this with a bespoke cohort-based Advanced Training program in Statistics and Machine Learning (StatML-AT). StatML-AT has been developed from our experience and in partnership with industry. It will be responsive to emerging technologies and equip our students with the practical skills required to transform how data is used. It will be delivered by our outstanding academics from both institutions alongside with industry leaders to ensure that students receive training in cutting edge technologies, along with the latest ideas in ethics, responsible innovation, sustainability and entrepreneurship. This will be complemented by industrial and academic placements to allow the students to develop their own international network and produce high-impact research. Together, StatML and its partners will train 90+ students over 5 cohorts. More than half of these will be funded from external sources, including 25+ by industry, representing excellent value for money. Our diverse cohorts will benefit from a unique and responsive training program combining academic excellence, industry engagement, and interdisciplinary culture. This will make StatML a vibrant research environment inspiring the next methodological advancements to transform the use of data and AI across industry and society.