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到某个空间区域、某个时间间隔或两者的数据。此类数据在大型环境或流行病学研究中越来越常见。例如，在罕见疾病的例子中，探索疾病发病率的空间结构需要收集很长一段时间（通常是几十年）的病例。数据通常以地理区域邮政编码或人口普查计数区域细分的病例数形式出现。如果定期收集数据，例如在人口普查中每五年收集一次，则数据会在空间和时间上进行汇总。流行病学研究的目标之一是探索某一地理区域疾病发病率强度表面的结构。目的是识别任何表明疾病发病率高于预期的结构。这种“热点”本身可能是由于环境来源（例如地下水中的砷影响肾癌的发病率）或恶化/改善的工业条件（例如石棉的废弃而导致间皮瘤的发病率）。这种聚合的时空数据增加了复杂性，因为地理区域的边界本身会随着时间的推移而变化。结果是，在整个研究期间，我们无法说出研究中任何细分的病例数。此外，例如，如果研究区域内的个人居住历史随时间变化，则数据本身可能会被误测。所提出的研究考虑开发统计算法来分析这种混乱的不完整数据。这包括将现有的局部 EM 算法扩展到一组 EMS 算法，其中 S 步不再简单地由局部似然中核的选择决定，而是现在可能取决于我们如何在分层贝叶斯模型中建模相关结构。通过高斯马尔可夫随机场近似和稀疏矩阵计算获得计算效率。方法依赖于将数据建模为新颖的根高斯 Cox 过程，扩大平方根链接函数的选择，将允许将集成的嵌套拉普拉斯近似扩展到聚合数据。所提出的所有方法都将允许对已知错误测量的数据进行分析。