There are tremendous demands for advanced statistical methodology to make scientific sense of the deluge of data emerging from the data revolution of the 21st Century. Huge challenges in modelling, computation, and statistical algorithms have been created by diverse and important questions in virtually every area of human activity. CoSInES will create a step change in the use of principled statistical methodology, motivated by and feeding into these challenges. Much of our research will develop and study generic methods with applicability in a wide-range of applications. We will study high-dimensional statistical algorithms whose performance scales well to high-dimensions and to big data sets. We will develop statistical theory to understand new complex models stimulated from applications. We will produce methodology tailored to specific computational hardware. We will study the statistical and algorithmic effects of mis-match between data and models. We shall also build methodology for statistical inference where privacy constraints mean that the data cannot be directly accessed. CoSInES willl also focus on two major application domains which will form stimulating and challenging motivation for our research: Data-centric engineering, and Defence and Security. To maximise the impact and speed of translation of our research in these areas, we will closely partner the Alan Turing Institute which is running large programmes in these areas funded respectively by the Lloyd's Register Foundation and GCHQ. Data is providing a disruptive transformation that is revolutionising the engineering professions with previously unimagined ways of designing, manufacturing, operating and maintaining engineering assets all the way through to their decommissioning. The Data centric engineering programme (DCE) at the Alan Turing Institute is leading in the design and operation of the worlds very first pedestrian bridge to be opened and operated in a major international city that will be completely 3-D printed. Fibre-optic sensors embedded in the structure will provide continuous streams of data measuring the main structural properties of the bridge. Unique opportunities to monitor and control the bridge via "digital twins" are being developed by DCE and this is presenting enormous challenges to existing applied mathematical and statistical modelling of these complex structures where even the bulk material properties are unknown and certainly stochastic in their values. A new generation of numerical inferential methods are being demanded to support this progress. Within the Defence and Security domain, there are many statistical challenges emerging from the need to process and communicate big and complex data sets, for example within the area of cyber-security. The virtual world has emerged as a dominant global marketplace within which the majority of organisations operate. This has motivated nefarious actors - from "bedroom hackers" to state-sponsored terrorists - to operate in this environment to further their economic or political ambitions. To counter this threat, it is necessary to produce a complete statistical representation of the environment, in the presence of missing data, significant temporal change, and an adversary willing to manipulate socio and virtual systems in order to achieve their goals. As a second example, to counter the threat of global terrorism, it is necessary for law-enforcement agencies within the UK to share data, whilst rigorously applying data protection laws to maintain individuals' privacy. It is therefore necessary to have mathematical guarantees over such data sharing arrangements, and to formulate statistical methodologies for the "penetration testing" of anonymised data.