The Centre for Doctoral Training MAC-MIGS will provide advanced training in the formulation, analysis, and implementation of state-of-the-art mathematical and computational models. The vision for the training offered is that effective modern modelling must integrate data with laws framed in explicit, rigorous mathematical terms. The CDT will offer 76 PhD students an intensive 4-year training and research programme that equips them with the skills needed to tackle the challenges of data-intensive modelling. The new generation of successful modelling experts will be able to develop and analyse mathematical models, translate them into efficient computer codes that make best use of available data, interpret the results, and communicate throughout the process with users in industry, commerce and government. Mathematical and computational models are at the heart of 21st-century technology: they underpin science, medicine and, increasingly, social sciences, and impact many sectors of the economy including high-value manufacturing, healthcare, energy, physical infrastructure and national planning. When combined with the enormous computing power and volume of data now available, these models provide unmatched predictive tools which capture systematically the experimental and observational evidence available. Because they are based on sound deductive principles, they are also the only effective tool in many problems where data is either sparse or, as is often the case, acquired in conditions that differ from the relevant real-world scenarios. Developing and exploiting these models requires a broad range of skills - from abstract mathematics to computing and data science - combined with expertise in application areas. MAC-MIGS will equip its students with these skills through a broad programme that cuts across disciplinary boundaries to include mathematical analysis - pure, applied, numerical and stochastic - data-science and statistics techniques and the domain-specific advanced knowledge necessary for cutting-edge applications. MAC-MIGS students will join the broader Maxwell Institute Graduate School in its brand-new base located in central Edinburgh. They will benefit from (i) dedicated academic training in subjects that include mathematical analysis, computational mathematics, multi-scale modelling, model reduction, Bayesian inference, uncertainty quantification, inverse problems and data assimilation, and machine learning; (ii) extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships; (iii) outstanding early-career training, with a strong focus on entrepreneurship; and (iv) a dynamic and forward-looking community of mathematicians and scientists, sharing strong values of collaboration, respect, and social and scientific responsibility. The students will integrate a vibrant research environment, closely interacting with some 80 MAC-MIGS academics comprised of mathematicians from the universities of Edinburgh and Heriot-Watt as well as computer scientists, engineers, physicists and chemists providing their own disciplinary expertise. Students will benefit from MAC-MIGS's diverse network of more than 30 industrial and agency partners spanning a broad spectrum of application areas: energy, engineering design, finance, computer technology, healthcare and the environment. These partners will provide internships, development programmes and research projects, and help maximise the impact of our students' work. Our network of academic partners representing ten leading institutions in the US and Europe, will further provide opportunities for collaborations and research visits.

SECURE is a network of statisticians, modellers and environmental scientists and our aim is to grow a shared vision of how to describe and quantify environmental change to assist in decision making. Understanding and forecasting environmental changes are crucial to the development of strategies to mitigate against the impacts of future events. Communications and decision making around environmental change are sometimes troubled by issues concerning the weight of evidence, the nature and size of uncertainties and how both are described. Evidence for environmental change comes from a number of sources, but key to this proposal is the optimal use of data (from observational, regulatory monitoring and earth observations platforms such as satellites and mobile sensors) and models (process and statistical). A robust and reliable evidence base is key in the decision making process, informed by powerful statistical models and the best data. This proposal will deliver the statistical tools to support decision making. Many environmental challenges related to change require statistical modelling and inferential tools to be developed to understand the drivers and system responses which may be direct or indirect and linked by feedback and lags. The character of environmental data is changing as new technologies (e.g. sensor networks offering high resolution data streams) are developed and become more widely accessible. Emerging sensor technology is able to deliver enhanced dynamic detail of environmental systems at unprecedented scale and . There is also an increasing public engagement with environmental science, through citizen science. Increasing use of citizen science observatories will present new statistical challenges, since the sampling basis of such observations will most likely be preferential and not directed, be of varying quality and collected with different effort. Fusion of the different streams of data will be challenging but essential in terms of informing society and regulators alike about change. Linkage of the different data sources, and the challenges of dealing with big data, in the environmental sphere lie in drawing together diverse, high-throughput data sources, analysing, aggregating and integrating the signals with models and then ultimately using the data-model system to address complex and shifting environmental change issues in support of decision making. Key to success lies in generating digestible outputs which can be disseminated and critiqued across academia, policy-makers and other stakeholders. In climate change, food security, ecosystem resilience, sustainable resource use, hazard warning and disaster management there are new high-volume data sources, including crowd sourced streams, which present problems and untapped opportunities around data management, synthesis, communication and real-time decision-support. Our research will involve: improving modelling and communication tools concerning uncertainty and variability, which are ubiquitous in many environmental data sources; developing and extending modelling capabilities to deal with multi-scale issues, specifically integrating over the different spatial and temporal scales of the data streams, and the derived timescales of model outputs; exploring the power and limitations of recent statistical innovations applied to environmental change issues and finally reflecting on new technologies for visualisation and communication.