An Ordinary Least Squares (OLS) Solution to Handling Spatial Autocorrelation Latent in Georeferenced Data

该项目的总体目标是利用与地理参考数据（即标记到地球表面位置的数据）地理相关的数学量。 它的重要性在于它能够让科学家们使用分布在地球各区域的各种过程的更复杂和更现实的模型。 研究的本质是由一个认识，莫兰系数（空间自相关指数）可以分解成正交的地图模式分量的动机。 这种分解将Moran系数直接与标准线性回归相关联，其中相应的特征向量可以用作预测因子。 其代数结构与约束最大似然估计（REML）非常相似。 分析工作将辅以数值方法，将侧重于马尔可夫链蒙特卡罗（MCMC）分析，经验贝叶斯分析和模拟实验。基本知识的进步将是描述包含正空间自相关的自动泊松分布，从而更好地理解如何解释地理参考的空间数据（例如大多数卫星数据）。 这项研究对科学知识的进步具有重要意义，因为它将建立将地理参考数据转换为增值信息所需的统计理论。 该项目至少以三种不同的方式处理有关的社会关切：（1）它将有助于卫星数据和社会科学数据的结合，这是美国航天局目前的一个目标;（2）它将有助于揭开空间统计的神秘面纱，使人们能够在今天必须查看方程式的地方查看地图;以及（3）通过用易于理解的传统回归术语重新描述这一主题，将使空间数据统计的很大一部分更容易为更多受众所用。因此，该研究将使社会更好地了解这些问题，如EPA追求的超级基金补救策略，小面积的估计方案正在实施的各种联邦数据收集机构，和国家卫生组织，如NCI的地理疾病集群评估。

The overall objective of this project is to exploit mathematical quantities related to the geography of georeferenced data-that is, data that are tagged to locations on the earth's surface. Its importance lies in its ability to allow scientists to work with more sophisticated and realistic models of various kinds of processes distributed across regions of the earth. The essence of the research is motivated by a recognition that the Moran Coefficient (a spatial autocorrelation index) can be decomposed into orthogonal map pattern components. This decomposition relates the Moran Coefficient directly to a standard linear regression, in which corresponding eigenvectors can be used as predictors. The algebraic structure is very similar to that of restricted maximum likelihood (REML) estimation. The analytical work will be complemented by numerical approaches that will focus on Markov Chain Monte Carlo (MCMC) analysis, empirical Bayes analysis, and simulation experiments. The basic knowledge advancement will be a description of auto-Poisson distributions containing positive spatial autocorrelation, and thus, a better understanding of how to interpret spatial data that are georeferenced (e.g. most satellite data). This research is significant to the advancement of scientific knowledge because it will establish the statistical theory necessary to convert georeferenced data into value-added information. The project addresses relevant societal concerns in at least three different ways: (1) it will contribute to an integration of satellite and social science data, a current goal of NASA; (2) it will help demystify spatial statistics, allowing maps to be viewed where today equations must be viewed; and, (3) it will make a sizeable part of statistics for spatial data more accessible to a larger audience by recasting this topic in conventional regression terms that are readily understood. Thus, the research will enable society's better understanding of such concerns as superfund remediation strategies pursued by the EPA, small-area estimation programs being implemented by various federal data collection agencies, and geographic disease cluster evaluations by national health organizations such as the NCI.