Computationally Intensive Methods for Large Spatio-Temporal Data Sets

拟议的研究涉及在一个空间区域、一段时间内或两者兼而有之的汇总数据。这类数据在大型环境或流行病学研究中越来越普遍。例如，以罕见疾病为例，探索疾病发病率的空间结构需要在很长一段时间（通常是几十年）内收集病例。这些数据通常以地理区域、邮政编码或人口普查枚举区域细分的病例计数的形式出现。如果数据是定期收集的，比如像人口普查那样每五年收集一次，那么数据在空间和时间上都是汇总的。流行病学研究的目标之一是探索一个地理区域内疾病发病率的强度面结构。目的是确定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）或工业条件的恶化/改善（例如，停止使用石棉对间皮瘤发病率的影响）。这种聚合的时空数据具有额外的复杂性，因为地理区域的边界本身可以随着时间的推移而变化。结果是，在整个研究期间我们不能说研究中任何细分的病例数是多少。此外，如果研究区域内的个人居住历史随时间而变化，数据本身可能会被错误测量。提出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。这包括将现有的局部em算法扩展为一组EMS算法，其中s步不再简单地由局部似然中的核的选择决定，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来提高计算效率。方法依赖于将数据建模为一个新的根高斯Cox过程，拓宽了平方根链接函数的选择将允许集成嵌套拉普拉斯近似扩展到聚合数据。所有提出的方法都将允许对已知测量错误的数据进行分析。

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.