Computationally Intensive Methods for Large Spatio-Temporal Data Sets

大型时空数据集的计算密集型方法

• 批准号: RGPIN-2018-04604
• 负责人: Stafford, James
• 金额: $ 2.91万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765691
• 关键词: Computationally; Intensive; Methods; Large; Spatio

The proposed research concerns data that has been aggregated to fall within a spatial region, an interval of time or both. Such data is increasingly common in large environmental or epidemiological studies. For example, in the instance of a rare disease exploring the spatial structure of disease incidence requires collecting cases over a long period of time often decades. The data usually comes in the form of case counts for subdivisions of a geographic region postal codes or census enumeration areas. If the data is collected periodically, say every five years as in the case of a census, then the data is aggregated in both space and time. One goal of an epidemiological study is to explore the structure of an intensity surface for disease incidence over a geographic region. The objective is to identify any structure that would indicate a higher than expected incidence of disease. Such a “hotspot” may itself be due to an environmental source (e.g. arsenic in ground water affecting the incidence of kidney cancer) or worsening/improving industrial conditions (e.g. the disuse of asbestos on the incidence of mesothelioma). Such aggregated spatio-temporal data has the added complexity that the boundaries of geographic regions can themselves change over time. The result is that over the period of entire study we can't say what the case count is for any subdivision within the study. In addition, the data itself may be mismeasured if, for example, an individuals residential history within the study region varies over time.The research proposed considers the development of statistical algorithms for the analysis of such messy incomplete data. This includes broadening an existing class of local-EM algorithms to a set of EMS algorithms where the S-step is no longer simply dictated by the choice of kernel in the local likelihood but may now depend on how we model the correlation structure within a hierarchical Bayesian model. Computational efficiency is gained through Gauss Markov random field approximations and sparse matrix computations. Methods rely on modeling the data as a novel root Gaussian Cox process broadening the choice of the square root link function will allow integrated nested Laplace approximations to be extended to aggregated data. All methods proposed will allow for the analysis of data that is known to be mismeasured.

拟议的研究涉及已汇总的数据属于空间区域，时间间隔或两者兼而有之。在大型环境或流行病学研究中，这种数据越来越普遍。例如，如果探索疾病事件的空间结构的罕见疾病，则需要在很长一段时间内经常收集病例。数据通常以案例计数的形式出现，用于地理区域邮政法规或人口普查区域的细分。如果定期收集数据，则每五年（如普查），则数据在时空和时间均已汇总。流行病学研究的目标之一是探索地理区域内疾病发病率的强度表面的结构。目的是确定任何表明高于预期疾病事件的结构。这样的“热点”本身可能是由于环境来源（例如影响肾癌事件的地下水中的砷）或担心/改善工业条件（例如，在间皮瘤事件中废除石棉的废弃）。这种汇总的时空数据具有额外的复杂性，即地理区域的边界本身可以随着时间而变化。结果是，在整个研究期间，我们不能说研究中的任何细分是什么。此外，如果例如，随着时间的流逝，研究区域内的个人居民历史上的居民历史上的历史可能会导致数据本身不予以管理。拟议中的研究考虑了统计算法的发展，以分析这种混乱的不完整数据。这包括将现有的一类局部EM算法扩大到一组EMS算法，在该算法中，S-step不再简单地由本地可能性中的内核选择决定，但现在可能取决于我们如何建模层次结构贝叶斯模型中的相关结构。通过高斯马尔可夫随机场近似和稀疏矩阵计算获得了计算效率。方法依赖于将数据建模为一种新型的根高斯Cox过程，扩大了平方根链路函数的选择将允许将集成的嵌套拉普拉斯近似值扩展到聚合数据。提出的所有方法将允许分析已知已知的数据。