SAMBa aims to create a generation of interdisciplinary mathematicians at the interface of stochastics, numerical analysis, applied mathematics, data science and statistics, preparing them to work as research leaders in academia and in industry in the expanding world of big models and big data. This research spectrum includes rapidly developing areas of mathematical sciences such as machine learning, uncertainty quantification, compressed sensing, Bayesian networks and stochastic modelling. The research and training engagement also encompasses modern industrially facing mathematics, with a key strength of our CDT being meaningful and long term relationships with industrial, government and other non-academic partners. A substantial proportion of our doctoral research will continue to be developed collaboratively through these partnerships. The urgency and awareness of the UK's need for deep quantitative analytical talent with expert modelling skills has intensified since SAMBa's inception in 2014. Industry, government bodies and non-academic organisations at the forefront of technological innovation all want to achieve competitive advantage through the analysis of data of all levels of complexity. This need is as much of an issue outside of academia as it is for research and training capacity within academia and is reflected in our doctoral training approach. The sense of urgency is evidenced in recent government policy (cf. Government Office for Science report "Computational Modelling, Technological Futures, 2018"), through the EPSRC CDT priority areas of Mathematical and Computational Modelling and Statistics for the 21st century as well as through our own experience of growing SAMBa since 2014. We have had extensive collaboration with partners from a wide range of UK industrial sectors (e.g. agri-science, healthcare, advanced materials) and government bodies (e.g. NHS, National Physical Laboratory, Environment Agency and Office for National Statistics) and our portfolio is set to expand. SAMBa's approach to doctoral training, developed in conjunction with our industrial partners, will create future leaders both in academia and industry and consists of: - A broad-based first year developing mathematical expertise across the full range of Statistical Applied Mathematics, tailored to each incoming student. - Deep experience in academic-industrial collaboration through Integrative Think Tanks: bespoke problem-formulation workshops developed by SAMBa. - Research training in a department which produces world-leading research in Statistical Applied Mathematics. - Multiple cohort-enhanced training activities that maximise each student's talents and includes mentoring through cross-cohort integration. - Substantial international opportunities such as academic placements, overseas workshops and participation in jointly delivered ITTs. - The opportunity for co-supervision of research from industrial and non-maths academic supervisors, including student placements in industry. This proposal will initially fund over 60 scholarships, with the aim to further increase this number through additional funding from industrial and international partners. Based on the CDT's current track record from its inception in 2014 (creating 25 scholarships to add to an initial investment of 50), our target is to deliver 90 PhD students over the next five years. With 12 new staff positions committed to SAMBa-core areas since 2015, students in the CDT cohort will benefit from almost 60 Bath Mathematical Sciences academics available for lead supervisory roles, as well as over 50 relevant co-supervisors in other departments.

Together with industrial partners, we have established that there is a strong unmet demand for individuals with expertise in the combination of statistics, applied mathematics, computation, and the collaborative problem solving skills required to acquire application area knowledge. Consider, for example, aircraft structural design, where statistical methods have recently been approved in the certification of aircraft, complementing traditional experimental testing. This ushers in a change in possible design methodology, but creates a corresponding gap for the necessary talent in the workforce: scientists with knowledge of materials, computational methods and statistics. Such individuals are needed to sustain the UK's global competitive advantage, industrially and academically. We propose a world leading and innovative cohort-driven centre for doctoral training at the interface of Statistics and Applied Mathematics: Statistical Applied Mathematics at Bath (SAMBa). Modern mathematical models describing real world applications must incorporate randomness and data in a variety of ways in order to improve their ability to predict complex behaviour and describe empirical observations. Traditionally, deterministic applied mathematics and statistical methods have taken different approaches in modelling observed phenomena. More recently, we have seen that this is proving to be a hindrance to the competitiveness of British mathematics, especially when taking account of the enormous scope for research with genuine real-world impact. SAMBa will create a new generation of interdisciplinary mathematicians, both for academic careers as well as for insertion into British industry. Their primary strengths will be their problem solving ability and their fearlessness of barriers separating mathematical modelling and modern statistics. Moreover, the implementation of this CDT will promote a novel way of educating UK PhD students within the mathematical sciences, in which there is horizontal cross-disciplinary and industrial integration through CDT activities. The central mechanism by which this horizontal integration will occur will be through week-long Integrative Think Tanks (ITT), which share similarities with sandpits. These ITTs will be supported by an array of new courses that span a spectrum including statistics, stochastic simulation and applied mathematics. SAMBa will enrol ten students per year on a four-year study programme. The first year will focus on the new courses and in the formation of research themes, as well as developing cohort integration. ITTs will occur at the end of the first and second semesters during the first year of study, and will give students the opportunity to learn how to formulate problems and structure their approach to problem solving. ITTs will be intensive activities, managed by academic staff together with interdisciplinary and industrial leaders. Students in later years will participate in one ITT per year with a view to enhancing the PhD cohort experience. The expected outcomes of the ITTs will be: to provide real experiences in approaches to problem solving, to promote cross-fertilisation of ideas and expertise through horizontal integration, to build a cohesive PhD student cohort, to catalyse new collaborations, and to provide a source of PhD thesis projects. It is expected that most, but not all, PhD thesis problems and supervisory teams will emerge from ITTs. PhD students will also run a symposium series to prepare for, and subsequently reinforce, the ITT experience as well as to develop the students' sense of research empowerment. Students in SAMBa will be awarded an M.Res. after one year, subject to successful assessment. In addition, we will strongly encourage three month industrial or cross-disciplinary academic placements. These placements will enhance the horizontal integration and are a natural extension of our long-standing and thriving BSc an MSc placement scheme.