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

当在环境、生态或流行病学设置等应用中分析时空数据时，检测空间和/或时间上的突变可以使我们深入了解系统的潜在机制，并可以对过程的进化和未来状态的解释产生重大影响。另外，识别异常对于不曲解数据趋势也同样重要。该项目的目标包括研究分析时空数据的方法，并进一步扩展这些方法，在文献中存在空白的地方，寻求开发一套强大的统计工具来解释这些数据集。我们还考虑了涉及非平稳性的更复杂的情况。特别是，我们将考虑数据的空间和时间元素如何相互作用，当我们能够检测到变化点或异常时，我们如何容易地对它们进行分类，以及在空间和时间元素之间是否可以分离平稳性。因此，我们希望能够用我们开发的方法检测空间随时间的局部变化。在博士学位的第一部分，将进行全面的文献综述，以评估在时间序列和空间模型中以及在适用的情况下，在时空域中的artin变化点和异常检测的状态。如果发现了差距，或者有发展或适应这些方法的余地，我们希望在时空领域扩展和实施它们，展示所考虑的方法的问题和局限性，然后我们是否可以修复或改进它们。考虑到即使在时间或空间领域仍存在未解决的挑战，考虑如何在我们寻求将两者结合起来时克服这些挑战，对于在更复杂的情况下取得进展至关重要。因此，首先考虑多变量时间序列的扩展和方法，对时间序列中的多变化点检测将是一个很好的起点，从而引导到高维数据分析。在第一年，我计划通过apts课程进行统计建模和计算方面的额外培训，以补充我的数学背景。此外，我希望通过阅读课程培养我在阅读和批判性分析学术论文方面的研究技能，这也将拓宽我在研究领域的学科知识。我也在学习机器学习和科学计算的模块，以进一步发展我的研究软件技能。通过这种方式，我将获得高效编程的经验，并能够利用高性能计算来分析复杂的数据集，拟合统计模型，并在我的研究中有效地将结果可视化。

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.