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

为时空建模中出现的问题开发有效的统计工具

• 批准号: 2279484
• 金额: --
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2279484
• 关键词: Developing; efficient; statistical; tools; problems

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.

当分析时空数据的应用，如在环境，生态，或流行病学设置，检测空间和/或时间的突然变化，使我们深入了解一个系统的基本机制，并可以在解释的演变和未来状态的过程中产生重大影响。另外，识别异常与不误解数据趋势同样重要。该项目的目标包括研究分析时空数据的方法，并在文献存在空白的情况下进一步扩展这些方法，以期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，以及空间和时间元素之间的平稳性是否可分离。作为一个结果，我们希望能够检测localisedchanges在空间随着时间的推移与我们开发的methods.In博士学位的第一部分，将进行全面的文献综述，以评估最先进的变点和异常检测的时间序列和空间模型，并在适用的情况下，在时空域。如果发现了差距，或者有开发或调整这些方法的余地，我们希望在时空域中扩展和实施这些方法，证明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。鉴于即使是在时间或空间领域也仍然存在尚未解决的挑战，在我们寻求将时间和空间两个领域结合起来时，考虑如何克服这些挑战对于在更复杂的局势中取得进展至关重要。因此，首先考虑多元时间序列的扩展和时间序列中多个变点检测的方法将是一个很好的起点，以引入更高维度的数据分析。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。除此之外，我希望通过阅读课程来发展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。我还参加了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。通过这一点，我将获得有效编程的经验，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，并在我的研究中进一步有效地可视化结果。