Developing efficient statistical tools for problems arising in spatio-temporal modelling

When analysing spatio-temporal data in applications such as in environmental, ecological, or epidemiological
settings, detecting abrupt changes over space and or time gives us insight into the underlying mechanics of a system
and can have a significant impact in the interpretation of the evolution and future state of the process. Alternatively
identifying anomalies is of equal importance to not misinterpret trends in the data. The aims of the project include
looking at methods that analyse spatio-temporal data and expand on these further, where gaps in the literature exist,
look to developing a set of robust statistical tools to interpret these datasets. We also consider more complex
situations involving non-stationarity. In particular we will consider how the space and time elements of the data
interact, and when we are able to detect change points or anomalies how easily can we classify them and if the
stationarity is separable between the space and time elements. As an outcome we hope to be able to detect localised
changes in space over time with our developed methods.
In the first part of the PhD a comprehensive literature review will be undertaken to assess the state of the art
in change-point and anomaly detection in time series and spatial model and where applicable, in the spatio-temporal
domain. Where gaps are identified or there is scope to develop or adapt these methods we hope to extend and
implement them in the spatio-temporal domain, demonstrate what the problems and the limitations of the methods
considered are, and then if we can fix or improve on them. Given that there are still unresolved challenges even in
just the temporal or spatial domains, considering how those challenges will be overcome when we look to combine
both will be crucial to making progress in the more complex situation. Thus, firstly considering the extensions to
multivariate time series and methods for multiple change-point detection in time series will be a good start ing point,
to lead into higher dimensional data analysis.
Over the first year I plan to undertake additional training in statistical modelling and computation through the
APTS courses, to complement my background in mathematics. Further to this I hope to develop my research skills in
reading and critically analysing academic paper through the reading courses, that will also broaden my subject
knowledge in my area of research. I am also taking modules in machine learning and scientific computing to further
develop my research software skills. Through this I will gain experience in efficiently programming and being able to
utilise high performance computing to analyse complex datasets, fit statistical models and effectively visualise the
results in my research further down the line.

Combining specialised modelling techniques with complex data analysis in order to deliver prediction with quantified uncertainties lies at the heart of many of the major challenges facing UK industry and society over the next decades. Indeed, the recent Government Office for Science report "Computational Modelling, Technological Futures, 2018" specifies putting the UK at the forefront of the data revolution as one of their Grand Challenges.

The beneficiaries of our research portfolio will include a wide range of UK industrial sectors such as the pharmaceutical industry, risk consultancy, telecommunications and advanced materials, as well as government bodies, including the NHS, the Met Office and the Environment Agency.

Examples of current impactful projects pursued by students and in collaboration with stake-holders include:

- Using machine learning techniques to develop automated assessment of psoriatic arthritis from hand X-Rays, freeing up consultants' time (with the NHS).

- Uncertainty quantification for the Neutron Transport Equation improving nuclear reactor safety (co-funded by Wood).

- Optimising the resilience and self-configuration of communication networks with the help of random graph colouring problems (co-funded by BT).

- Risk quantification of failure cascades on oil platforms by using Bayesian networks to improve safety assessment for certification (co-funded by DNV-GL).

- Krylov regularisation in a Bayesian framework for low-resolution Nuclear Magnetic Resonance to assess properties of porous media for real-time exploration (co-funded by Schlumberger).

- Machine learning methods to untangle oceanographic sound data for a variety of goals in including the protection of wildlife in shipping lanes (with the Department of Physics).

Future committed partners for SAMBa 2.0 are: BT, Syngenta, Schlumberger, DNV GL, Wood, ONS, AstraZeneca, Roche, Diamond Light Source, GKN, NHS, NPL, Environment Agency, Novartis, Cytel, Mango, Moogsoft, Willis Towers Watson.

SAMBa's core mission is to train the next generation of academic and industrial researchers with the breadth and depth of skills necessary to address these challenges. SAMBa's most sustained impact will be through the contributions these researchers make over the longer term of their careers. To set the students up with the skills needed to maximise this impact, SAMBa has developed a bespoke training experience in collaboration with industry, at the heart of its activities. Integrative Think Tanks (ITTs) are week-long workshops in which industrial partners present high-level research challenges to students and academics. All participants work collaboratively to formulate mathematical
models and questions that address the challenges. These outputs are meaningful both to the non-academic partner, and as a mechanism for identifying mathematical topics which are suitable for PhD research. Through the co-ownership of collaboratively developed projects, SAMBa has the capacity to lead industry in capitalising on recent advances in mathematics. ITTs occur twice a year and excel in the process of problem distillation and formulation, resulting in an exemplary environment for developing impactful projects.

SAMBa's impact on the student experience will be profound, with training in a broad range of mathematical areas, in team working, in academic-industrial collaborations, and in developing skills in communicating with specialist and generalist audiences about their research. Experience with current SAMBa students has proven that these skills are highly prized: "The SAMBa approach was a great template for setting up a productive, creative and collaborative atmosphere. The commitment of the students in getting involved with unfamiliar areas of research and applying their experience towards producing solutions was very impressive." - Dr Mike Marsh, Space weather researcher, Met Office.