Methodology For Analyzing Spatial Data

最近，相当大的兴趣开始聚焦于空间数据问题。统计学家找到了一个令人兴奋的机会来扩展目前以描述性总结和特别推理程序为主的分析曲目。将形式化的随机建模和由此产生的完全推理引入到空间数据的分析中，变得很有吸引力。完全基于模型的方法在提供足够灵活的框架和在这样的框架内拟合模型方面都提供了挑战。所提出的研究考虑了三个这样的挑战问题。它们是：(I)当对从不同来源收集的相关变量感兴趣并且这些来源使用区域的不同区域分区时出现的未对齐的数据层的处理；(Ii)对于观测数据产生的二变量(以及更一般地，多变量)空间过程的处理，或者作为分层模型中的潜在(第二阶段)过程的处理；以及(Iii)在所谓的使用第一阶段或第二阶段高斯规范的地统计学角度内的大空间数据集的处理，提出了一种似然估计，其计算需要高维矩阵求逆。空间数据产生于许多应用领域。例如，在生态学和进化生物学中，对森林砍伐过程的调查是一个重要的领域。这种过程固有地表现出随时间演变的空间模式，因此与联邦在环境和全球变化(EGCH)中的战略利益有关。除了土地的自然特征外，利用社会经济信息来理解这一过程是很有意义的。在金融/房地产应用中，编制住宅物业价值指数是很有意义的。人们熟悉的格言“位置，位置，位置”预测了房价的空间关联。在流行病学中，人们试图确定疾病发病率的空间模式/聚集性，以便评估高危地区。吸毒率必须进行调整，以反映人口规模和暴露于风险因素的差异。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更高的结论。这项赠款资助下的研究建议使用概率建模来解决这些问题。目标是在这样的模型下进行适当的规范、拟合和绘图推理。

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.