We live in the age of data. Technology is transforming our ability to collect and store data on unprecedented scales. From the use of Oyster card data to improve London's transport network, to the Square Kilometre Array astrophysics project that has the potential to transform our understanding of the universe, Big Data can inform and enrich many aspects of our lives. Due to the widespread use of sensor-based systems in everyday life, with even smartphones having sensors that can monitor location and activity level, much of the explosion of data is in the form of data streams: data from one or more related sources that arrive over time. It has even been estimates that there will be over 30 billion devices collecting data streams by 2020. The important role of Statistics within "Big Data" and data streams has been clear for some time. However the current tendency has been to focus purely on algorithmic scalability, such as how to develop versions of existing statistical algorithms that scale better with the amount of data. Such an approach, however, ignores the fact that fundamentally new issues often arise when dealing with data sets of this magnitude, and highly innovative solutions are required. Model error is one such issue. Many statistical approaches are based on the use of mathematical models for data. These models are only approximations of the real data-generating mechanisms. In traditional applications, this model error is usually small compared with the inherent sampling variability of the data, and can be overlooked. However, there is an increasing realisation that model error can dominate in Big Data applications. Understanding the impact of model error, and developing robust methods that have excellent statistical properties even in the presence of model error, are major challenges. A second issue is that many current statistical approaches are not computationally feasible for Big Data. In practice we will often need to use less efficient statistical methods that are computationally faster, or require less computer memory. This introduces a statistical-computational trade-off that is unique to Big Data, leading to many open theoretical questions, and important practical problems. The strategic vision for this programme grant is to investigate and develop an integrated approach to tackling these and other fundamental statistical challenges. In order to do this we will focus in particular on analysing data streams. An important issue with this type of data is detecting changes in the structure of the data over time. This will be an early area of focus for the programme, as it has been identified as one of seven key problem areas for Big Data. Moreover it is an area in which our research will lead to practically important breakthroughs. Our philosophy is to tackle methodological, theoretical and computational aspects of these statistical problems together, an approach that is only possible through the programme grant scheme. Such a broad perspective is essential to achieve the substantive fundamental advances in statistics envisaged, and to ensure our new methods are sufficiently robust and efficient to be widely adopted by academics, industry and society more generally.

This project will propose an urban grammar to describe urban form and will develop artificial intelligence (AI) techniques to learn such a grammar from satellite imagery. Urban form has critical implications for economic productivity, social (in)equality, and the sustainability of both local finances and the environment. Yet, current approaches to measuring the morphology of cities are fragmented and coarse, impeding their appropriate use in decision making and planning. This project will aim to: 1) conceptualise an urban grammar to describe urban form as a combination of "spatial signatures", computable classes describing a unique spatial pattern of urban development (e.g. "fragmented low density", "compact organic", "regular dense"); 2) develop a data-driven typology of spatial signatures as building blocks; 3) create AI techniques that can learn signatures from satellite imagery; and 4) build a computable urban grammar of the UK from high-resolution trajectories of spatial signatures that helps us understand its future evolution. This project proposes to make the conceptual urban grammar computable by leveraging satellite data sources and state-of-the-art machine learning and AI techniques. Satellite technology is undergoing a revolution that is making more and better data available to study societal challenges. However, the potential of satellite data can only be unlocked through the application of refined machine learning and AI algorithms. In this context, we will combine geodemographics, deep learning, transfer learning, sequence analysis, and recurrent neural networks. These approaches expand and complement traditional techniques used in the social sciences by allowing to extract insight from highly unstructured data such as images. In doing so, the methodological aspect of the project will develop methods that will set the foundations of other applications in the social sciences. The framework of the project unfolds in four main stages, or work packages (WPs): 1) Data acquisition - two large sets of data will be brought together and spatially aligned in a consistent database: attributes of urban form, and satellite imagery. 2) Development of a typology of spatial signatures - Using the urban form attributes, geodemographics will be used to build a typology of spatial signatures for the UK at high spatial resolution. 3) Satellite imagery + AI - The typology will be used to train deep learning and transfer learning algorithms to identify spatial signatures automatically and in a scalable way from medium resolution satellite imagery, which will allow us to back cast this approach to imagery from the last three decades. 4) Trajectory analysis - Using sequences of spatial signatures generated in the previous package, we will use machine learning to identify an urban grammar by studying the evolution of urban form in the UK over the last three decades. Academic outputs include journal articles, open source software, and open data products in an effort to reach as wide of an academic audience as possible, and to diversify the delivery channel so that outputs provide value in a range of contexts. The impact strategy is structured around two main areas: establishing constant communication with stakeholders through bi-directional dissemination; and data insights broadcast, which will ensure the data and evidence generated reach their intended users.

This project's aim is to explore the economic effects of diverse teams and workplaces - and the wider role of urban diversity - specifically, on entrepreneurship and firm-level innovation and productivity in the UK. These are important issues that are under-explored, especially in the UK, largely because of data challenges. And exploring these issues in the way we set out will make a valuable contribution to the huge, ongoing public debates on equalities, diversity and inclusion - both in the UK and across the world. Our project will combine administrative microdata, novel online data sources and frontier methods in econometrics and data science. Specifically, we will match LinkedIn data on individuals (via the Diffbot knowledge graph) to companies, then to administrative firm-level data (the Business Structure Database, plus patents and other info). Working in secure settings, we will use name analysis tools to probabilistically identify gender and ethnicity, and would also gather information on nationality and country of birth. We will focus the resulting panels on sectors where we're confident LinkedIn has good coverage - likely to be strategically important industries like tech, finance and business services - and run our data through multiple quality checks. We will use various tools to get closer to causality, including instrumental variable strategies and using policy 'shocks' such as a) Brexit and subsequent policy events, and b) recent UK gender pay gap legislation. We will also deploy a robust set of technical safeguards to ensure individuals' privacy, publishing only non-disclosive results. The project will develop new knowledge in an important but under-researched set of topics. In the process it would also build a unique data platform that other researchers could use in the future. We will work together with leading industry, policy and civil society stakeholders with expertise on relevant concepts, data/methods and policy agendas. These enable the project to directly contribute to economic policymaking on productivity and its drivers, including the UK's emerging levelling-up agenda, while also informing business decision-making and speaking to important and ongoing wider public conversations. The project will generate a series of linked outputs: 1/ Three research papers, covering links between gender and ethnic diversity (and their intersections) and firm-level productivity, innovation and entrepreneurship. These would be published as working papers on high-profile platforms, then submitted to peer-reviewed journals. 2/ Additional non-technical, short-form content for each paper - blogs, policy briefs and so on; inviting our network / community to co-author or directly contribute whenever possible; 3/ The underlying data platform, which (subject to permissions) we will make available to other researchers as a safeguarded data asset; 4/ The wider network / community of researchers and practitioners we will build through the co-production process.

The last two decades have witnessed dramatic fluctuations in fertility levels, which were not predicted by demographers or government statisticians: Fertility significantly increased in the first decade of the 21st century, whereas it has declined thereafter. These fluctuations have significant implications for planning and policy making, at both national and local levels. For example, the fertility increase between 2001 and 2012 led to more than 60 thousand additional births in the UK annually. The causes of the recent fertility dynamics are unclear. Some researchers attribute the recent fluctuations in fertility levels to changes in fertility timing - i.e. the postponement or acceleration of childbearing. Others emphasise the importance of changes in population composition or changes in childbearing behaviour in response to past policy changes and the post-2008 economic recession. Birth registration data used by government statisticians at the Office for National Statistics (ONS), National Records of Scotland (NRS) and Northern Ireland Statistical Research Agency (NISRA) inform us about the total number of births and aggregated fertility measures; however, they do not provide information about childbearing trends by parity (birth order), which is critical to understanding and predicting fertility trends. High-quality large-scale longitudinal data provide the opportunity to conduct a detailed analysis of parity-specific fertility; for example, to determine whether fertility has recently declined because of the (further) postponement of childbearing and increased childlessness among women or because of declining family size among mothers (e.g. fewer third births). Childbearing is naturally a sequential process; decisions on having an additional child are likely to be evaluated on the basis of experience with previous children. Detailed analysis of fertility by parity will thus significantly enhance our ability to forecast future fertility. In this project we will harmonise census-linked administrative data from the ONS Longitudinal Study, Scottish Longitudinal Study, and Northern Ireland Longitudinal Study, together with survey data from the Understanding Society study. The project is thus novel in that it uses data from the all four UK constituent countries; focuses on the analysis of childbearing trends by birth order, and brings together experts in demography and statistical forecasting to develop better methods for fertility forecasting. First, we will calculate annual parity-specific fertility rates by UK country to determine how much changes in fertility levels are attributable to the changes in first, second, third or fourth births. We will then adjust fertility rates for characteristics of that population (e.g. place of birth, educational level) to determine how much a change in fertility levels in the UK over time is attributable to changes in population composition, and how much to changes in childbearing behaviour, possibly as a result of changing policies and economic environment. Finally, we will use information on parity-specific fertility to forecast future fertility levels in the UK using Bayesian methodology. The project will bring together researchers from the Universities of St Andrews and Southampton, as well as government statisticians from ONS, NRS, and NISRA, to work on an important policy-relevant topic. The project will greatly improve our understanding of the factors associated with changing fertility dynamics in the UK and will show how existing large-scale longitudinal datasets can be used for cross-country analysis of fertility by birth order. It will also significantly improve the methodology used for fertility forecasts for the UK and its constituent countries. A better understanding of the present childbearing trends and forecast of the future developments will be critical to inform the planning of demand for various public services (e.g., nurseries, school places and housing).

The Oxford-Warwick Statistics Programme will train a new cohort of at least 50 graduates in the theory, methods and applications of Statistical Science for 21st Century data-intensive environments and large-scale models. This is joint project lead by the Statistics Departments of Oxford and Warwick. These two departments, ranked first and second for world leading research in the last UK research assessment exercise, can provide a wonderful stimulating training environment for doctoral students in statistics. The Centre's pool of supervisors are known for significant international research contributions in modern computational statistics and related fields, contributions recognised by over 20 major National and International Awards since 2008. Oxford and Warwick attract students with competitively won international scholarships. The programme leaders expect to expand the cohort to 11 or 12 per year by bringing these students into the CDT, and raising their funding up to CDT-level using £188K in support from industry and £150K support from donors. The need to engage in large-scale highly structured statistical models has been recognized for some time within areas like genomics and brain-imaging technologies. However, the UK's leading industries and sciences are now also increasingly aware of the enormous potential that data-driven analysis holds. These industries include the engineering, manufacturing, pharmaceutical, financial, e-commerce, life-science and entertainment sectors. The analysis bottleneck has moved from being able to collect and record relevant data to being able to interpret and exploit vast data collections. These and other businesses are critically dependent on the availability of future leaders in Statistics, able to design and develop statistical approaches that are scalable to massive data. The UK can take a world lead in this field, being a recognized international leader in Statistics; and OxWaSP is ideally placed to realize the potential of this opportunity. The Centre is focused on a new type of training for a new type of graduate statistician in statistical methodology and computation that is scalable to big data. We will bring a new focus on training for research, by teaching directly from the scientific literature. Students will be thrown straight into reading and summarizing journal papers. Lecture-format contact is used sparingly with peer-to-peer learning central to the training approach. This is teaching and learning for research by doing research. Cohort learning will be enhanced via group visits to companies, small groups reproducing results from key papers, student-orientated paper discussions, annual workshops and a three-day off-site retreat. From the second year the students will join their chosen supervisors in Warwick and Oxford, five in each Centre coming together regularly for research group meetings that overlap Oxford and Warwick, for workshops and retreats, and teaching and mentoring of students in earlier years. The Centre is timely and ambitious, designed to attract and nurture the brightest graduate statisticians, broadening their skills to meet the new challenge and allowing them to flourish in a focused, communal, research-training environment. The strategic vision is to train the next generation of statisticians who will enable the new data-intensive sciences and industries. The Centre will offer a vehicle to bring together industrial partners from across the two departments to share ideas and provide an important perspective to our students on the research challenges and opportunities within commercial and social enterprises. Student's training will be considerably enhanced through the Centre's visits, lectures, internships and co-supervision from global partners including Amazon, Google, GlaxoSmithKline, MAN and Novartis, as well as smaller entrepreneurial start-ups Deepmind and Optimor.