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.

与连续数据的分析方法相比，空间离散数据的统计分析方法相对落后。这是一个显著的方法上的差距，因为前者通常是在地球科学和社会科学中收集的。例如，由于不同原因导致的死亡人数由整个美国的政府机构定期收集，并根据不同的人口统计变量（如年龄，性别和种族）进行分类。该项目旨在通过对地质统计离散数据模型进行全面研究来填补这一空白。该项目包括三个部分。首先，一类层次空间模型的开发，旨在改善目前使用的模型的调查确定的一些局限性。其中一些限制，涉及到这些模型所代表的空间关联结构，尤其是严重的，当数据主要由小的计数，正是在这种情况下，模型描述的离散数据是最需要的。这些新的模型和基于似然的方法来适应他们的属性进行了研究。其次，一类非层次空间模型的开发，旨在代表广泛的空间离散数据，而不仅仅是计数，具有空间关联结构，是互补的层次空间模型类。这类模型是通过分别对边缘和空间关联结构建模来构建的，使用类似于copula的方法。这些模型的属性和基于似然的方法来适应他们也进行了研究。第三，最近提出的贝叶斯方法来评估拟合优度的统计模型进行了研究，并在上述类别的模型探索使用其合理性。该方法基于在不同参数值下评估的关键量之间的分布特性，适用于分层和非分层模型。开发这样的方法是一个迫切的需要，因为正式的方法来评估模型的空间模型的充分性是众所周知的缺乏，空间数据是目前常规收集在许多地球和社会科学，如生态学，流行病学，人口学和地理，但方法的离散数据（如死亡人数）的分析是远远低于相应的方法分析连续数据（如温度）。研究者建议通过构建新的模型类别来填补这一空白，这些模型一方面改善了研究者对当前使用的模型所确定的一些限制，另一方面增加了模型所代表的数据模式。该项目还将制定方法，以评估新提出的模型的模型充分性，这是科学中普遍存在的任务，因为任何模型都不能完美地代表所研究的现象。在这个项目过程中开发的统计方法将对地球科学和社会科学产生直接的方法和实际影响，因为在这两个领域，空间离散数据是例行收集的，但分析这些数据的模型和方法却很少。拟议的模型类别将大大增加空间数据分析师可用的工具库，以及表示空间离散数据广泛行为的可能性。研究生将参与该项目，这将有助于他们在贝叶斯方法和空间统计的统计培训，以及对博士学位的未来的预测。他在德克萨斯大学圣安东尼奥分校的应用统计学专业学习。