Geostatistical Modeling of Spatial Discrete Data

空间离散数据的地统计建模

• 批准号: 1208896
• 负责人: Victor De Oliveira
• 金额: $ 15万
• 依托单位: University of Texas at San Antonio
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1208896&HistoricalAwards=false
• 关键词: Geostatistical; Modeling; Spatial; Discrete; Data

Statistical methods for the analysis of spatial discrete data are relatively underdeveloped when compared to methods for continuous data. This is a notable methodological gap since the former are routinely collected in the earth and social sciences. For instance, death counts due to different causes are collected on a regular basis by government agencies throughout the entire U.S. and classified according to different demographic variables, such as age, gender and race. This project aims at filling this gap by developing a comprehensive study of models for geostatistical discrete data. The project consists of three parts. First, a class of hierarchical spatial models is developed that seeks to ameliorate some limitations identified by the investigator of currently used models. Some of these limitations, relating to the spatial association structures representable by these models, are especially severe when the data consist mostly of small counts, precisely the case when models describing the discreteness of the data are most needed. The properties of these new models and likelihood based methods to fit them are studied. Second, a class of non-hierarchical spatial models is developed that seeks to represent a wide range of spatial discrete data, not just counts, having spatial association structures that are complementary to those in the class of hierarchical spatial models. The models in this class are constructed by separately modeling the marginal and spatial association structures, using an approach akin to copulas. The properties of these models and likelihood based methods to fit them are also studied. Third, a recently proposed Bayesian method to assess goodness-of-fit of statistical models is studied and its soundness for use in the aforementioned classes of models explored. The method, based on a distributional identity between pivotal quantities evaluated at different parameter values, is applicable to both hierarchical and non-hierarchical models. Developing such methods is a pressing need since formal methods to assess model adequacy of spatial models are notoriously lacking.Spatial data are nowadays routinely collected in many earth and social sciences, such as ecology, epidemiology, demography and geography, but methodology for the analysis of discrete data (say death counts) is much less developed than the corresponding methodology for the analysis of continuous data (say temperature). The investigator proposes to fill this gap by constructing new classes of models that on the one hand ameliorate some limitations identified by the investigator of currently used models, and on the other hand increase the data patterns represented by the models. The project will also develop methodology to assess model adequacy for the newly proposed models, a ubiquitous task in science since any model is an imperfect representation of the phenomenon under study. The statistical methodology developed in the course of this project would have immediate methodological and practical impacts on the earth and social sciences, where spatial discrete data are routinely collected but models and methods for their analysis are scarce. The proposed classes of models will substantially increase the arsenal of tools available to spatial data analysts and the possibility of representing a wide range of behaviors for spatial discrete data. Graduate students will be engaged in the project which will contribute to their statistical training in Bayesian methods and Spatial Statistics, as well as the projection into the future of the Ph.D. program in Applied Statistics at the University of Texas at San Antonio.

与连续数据的方法相比，用于分析空间离散数据的统计方法相对不发达。这是一个显着的方法论差距，因为前者通常在地球和社会科学中收集。例如，整个美国的政府机构定期收集由于不同原因而导致的死亡计数，并根据不同的人口变量（例如年龄，性别和种族）进行分类。该项目旨在通过对地统计离散数据的模型进行全面研究来填补这一空白。该项目由三个部分组成。首先，开发了一类层次空间模型，该模型旨在改善当前使用模型的研究者确定的一些局限性。与这些模型代表的空间关联结构有关的其中一些局限性在数据主要由小计数组成时，尤其是严重的，而当最需要描述数据离散性的模型时，则恰恰是这种情况。研究了这些新模型的属性和基于可能性的基于它们的可能性。其次，开发了一类非层次空间模型，该模型旨在代表广泛的空间离散数据，而不仅仅是计数，它们具有与层次空间模型类别中的空间关联结构互补的。该类别中的模型是通过使用类似于Copulas的方法分别对边际和空间关联结构进行建模来构建的。还研究了这些模型的属性和基于可能性的基于它们的可能性的方法。第三，研究了一种最近提出的贝叶斯方法来评估统计模型的合适性，并在所探索的上述模型类别中使用其健全性。该方法基于以不同参数值评估的关键量之间的分布身份，适用于层次结构和非层次模型。开发这种方法是一种紧迫的需求，因为众所周知，缺乏评估空间模型的模型是否足够的形式方法。如今，在许多地球和社会科学中常规收集了空间数据，例如生态学，流行病学，人口统计学和地理学，但是用于分析离散数据（例如，死亡计数）的方法比相应的数据分析（例如，多）的方法（例如，较少的数据）是相应的数据，而不是相应的数据，该方法是连续的。研究者建议通过构建新的模型类别来填补这一空白，从而改善研究人员对当前使用的模型确定的某些局限性，另一方面增加了模型代表的数据模式。该项目还将开发方法，以评估新提出的模型的模型充足性，这是科学中无处不在的任务，因为任何模型都是研究现象的不完美表示。在该项目过程中开发的统计方法将对地球和社会科学产生直接的方法论和实际影响，在这些方法中，通常会收集空间离散数据，但分析的模型和方法很少。所提出的类型类别将大大增加可用于空间数据分析师可用的工具的武器，并可能代表空间离散数据的广泛行为。研究生将参与该项目，该项目将有助于他们在贝叶斯方法和空间统计学方面的统计培训，以及对博士的未来的预测。德克萨斯大学圣安东尼奥分校的应用统计计划。