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

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When analysing spatio-temporal data in applications such as in environmental, ecological, or epidemiologicalsettings, detecting abrupt changes over space and or time gives us insight into the underlying mechanics of a systemand can have a significant impact in the interpretation of the evolution and future state of the process. Alternativelyidentifying anomalies is of equal importance to not misinterpret trends in the data. The aims of the project includelooking 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 complexsituations involving non-stationarity. In particular we will consider how the space and time elements of the datainteract, and when we are able to detect change points or anomalies how easily can we classify them and if thestationarity is separable between the space and time elements. As an outcome we hope to be able to detect localisedchanges 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 artin change-point and anomaly detection in time series and spatial model and where applicable, in the spatio-temporaldomain. Where gaps are identified or there is scope to develop or adapt these methods we hope to extend andimplement them in the spatio-temporal domain, demonstrate what the problems and the limitations of the methodsconsidered are, and then if we can fix or improve on them. Given that there are still unresolved challenges even injust the temporal or spatial domains, considering how those challenges will be overcome when we look to combineboth will be crucial to making progress in the more complex situation. Thus, firstly considering the extensions tomultivariate 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 theAPTS courses, to complement my background in mathematics. Further to this I hope to develop my research skills inreading and critically analysing academic paper through the reading courses, that will also broaden my subjectknowledge in my area of research. I am also taking modules in machine learning and scientific computing to furtherdevelop my research software skills. Through this I will gain experience in efficiently programming and being able toutilise high performance computing to analyse complex datasets, fit statistical models and effectively visualise theresults in my research further down the line.