Methodology For Analyzing Spatial Data

最近，人们开始对空间数据问题产生相当大的兴趣。 统计学家发现了一个令人兴奋的机会来扩展目前的分析剧目，这是由描述性摘要和特设推理程序占主导地位。 将正式的随机建模和由此产生的完整的推理变得可用，空间数据的分析变得有吸引力。 完全基于模型的方法在提供一个非常灵活的框架和在这样一个框架内拟合模型方面都提出了挑战。所提出的研究考虑了三个这样的挑战性问题：（i）处理不对齐的数据层，当有兴趣将从不同来源收集的变量相关联时，这些来源使用区域的不同区域分区，（ii）处理双变量（更一般地说，是多变量）空间过程，这些过程是由观测数据引起的，也是潜在的（第二阶段）在分层模型中处理，以及（iii）在所谓的"地质统计"视角内处理大型空间数据集，使用第一或第二阶段高斯规范，提出了一种可能性，其评估需要高维矩阵求逆。空间数据出现在许多应用领域。 例如，在生态学和进化生物学中，对森林砍伐过程的研究是一个重要领域。 这种过程内在地表现出随时间演变的空间格局，因此与联邦在环境和全球变化方面的战略利益（EGCH）有关。 除了土地的物理特征之外，利用社会经济信息来理解这一过程是很有意义的。 在金融/真实的房地产应用中，对住宅物业价值进行索引是有意义的。 众所周知的格言"位置，位置，位置"预测了房价的空间关联。在流行病学中，人们试图识别疾病发病率的空间模式/聚集，以评估高风险地区。 必须调整发病率，以反映人口规模和风险因素暴露的差异。 在所有这些应用中，对收集的数据进行简单的描述性总结是不够的。 相反，人们需要做出推断，例如，评估哪些因素可以解释森林砍伐，预测房屋上市时的价格，得出特定地区患特定疾病的风险明显较高的结论。 在这项资助下的研究提出了使用概率建模来解决这些问题。 适当的规格，拟合和绘图推理下，这种模式的目标。

Recently, considerable interest has begun to focus on spatial data problems. The statistician finds an excitingopportunity to expand the current analytical repertoire, which is dominated by descriptive summary and ad hoc inferenceprocedures. Bringing formal stochastic modeling and the resultant full inference which becomes available, to the analysis of spatial data becomes attractive. Fully model-basedapproaches offer challenges both in supplying a sufficientlyflexible framework and fitting models within such a framework.The proposed research considers three such challenging problems.They are (i) the handling of misaligned data layers which ariseswhen there is interest in relating variables which are collectedfrom different sources and these sources use different arealpartitions of a region, (ii) the handling of bivariate (and, moregenerally, multivariate) spatial processes arising for theobserved data or as latent (second stage) processes in a hierarchical model, and (iii) the handling of large spatialdatasets within the so-called "geostatistical" perspectivewhich, using first or second stage Gaussian specifications,presents a likelihood whose evaluation requires high-dimensional matrix inversion.Spatial data arises in many fields of application. For instance,in ecology and evolutionary biology, investigation of the processof deforestation is an important area. Such a process inherentlyexhibits spatial pattern which evolves over time and hence connects to federal strategic interest in environmental and global change(EGCH). It is of interest to use socioeconomic information inaddition to physical features of the land area to understand thisprocess. In financial/real estate applications it is of interestto index residential propery values. The familiar maxim, "location,location, location" anticipates spatial association in housing prices.In epidemiology one seeks to identify spatial patterns/clustering ofdisease incidence in order to assess areas of high risk. Incidencerates have to be adjusted to reflect differences in populationsize and exposure to risk factors. In all of these applications simple descriptive summary of the collected data will not be adequate. Rather, one needs to make inference, e.g., to assess which factors explain the deforestation, to predict the price of a home when it goes on the market, to conclude that a particular area is at a significantly higher risk for a particular disease. The research under this grant support proposes the use of probabilistic modeling to address these questions. Appropriate specification of, fitting of and drawing inference under such models are the objectives.