POWRE: Spatial Modeling of Count Data on a Lattice

9806051 Christman Research被提议为在空间点阵上观察到的计数数据开发新的统计模型和相关推断。 在经典的频率论方法中，有两种空间模型可用于网格上的计数数据：（1）条件指定模型，其中变量Y在单个站点的分布在函数上取决于变量在其周围邻域中的值，以及（2）同时指定模型，其中Y在整个区域上的联合分布是给定的。 建议的研究的目的是扩展的方法，条件指定的模型，以其他类型的自分布，不一定属于指数的家庭。 要研究的分布的具体类型是环境应用中常见的分层和混合模型。 除了确定条件自动模型具有有效联合分布的条件外，PI还将研究与基于指数族的模型相关的建模的几个方面。 例如，一个研究领域将是确定表达空间依赖性的适当手段，即通过哪个参数更好地表达空间依赖性。 PI将在1998 - 99学年在爱荷华州州立大学的政治学系担任客座教授时进行这项研究。 在爱荷华州州立大学，与拟议的研究有关的教师的专业知识和兴趣非常集中。 这些人非常适合带来新的想法，观察和专业知识，以解决在空间网格上建模计数数据的问题，特别是当它适用于环境问题时。 拟议的研究将使她能够发展统计和计算机技能，提高她的能力和研究潜力，并使她能够为统计科学的进步做出贡献，因为它涉及到空间建模。 她的研究能力的进一步发展将直接提高PI的教学能力，无论是在本科生和研究生水平，通过增加她自己的理解随机建模一般和空间建模特别。 建立她在建模方面的专业知识的机会将为她提供有效指导研究生和本科生的工具，并与其他研究人员在空间模型充分合作。 该项目由MPS多学科活动办公室（OMA）支持。

9806051 Christman Research is proposed to develop new statistical models and related inference for count data observed on spatial lattice. Two spatial models for count data on a lattice are available in the classical frequentist approach: (1) a conditionally specified model in which the distribution of the variable, Y at a single site, depends functionally on the values of the variable in its surrounding neighborhood, and (2) a simultaneously specified model in which the joint distribution of Y over the entire region is given. The purpose of the proposed research is to extend the methodology of conditionally specified models to other types of auto-distributions that do not necessarily belong to exponential families. The specific types of distributions that are to be studied are hierarchical and mixture models commonly seen in environmental applications. In addition to determining the conditions underwhich conditional auto-models have valid joint distributions, the PI will study several aspects of modeling that are also relevant to models based on exponential families. For example, one area of research will be to identify the appropriate means of expressing spatial dependence, i.e. through which parameter is it better expressed. The PI will perform this research while a visiting professor for academic year 1998-99 in the Department of Stateistics at Iowa State University. There exists at Iowa State University a remarkable concentration of expertise and interest in the faculty that is relevant to the proposed research. This collection of people is ideally suited to bringing new ideas, observations, and expertise to bear on the problems of modeling count data on a spatial lattice, especially as it applies to environmental problems. The proposed research will allow her to develop statistical and computer skills that increase her capabilities and research potential and will allow her to contribute to the advancement in the statistical sciences as it relates to spatial modeling. Further d evelopment in her research abilities will directly improve the PI's teaching capability both at the undergraduate and graduate levels by increasing her own understanding of stochastic modeling general and spatial modeling in particular. The opportunity to build her expertise in modeling would provide her with the tools to effectively mentor graduate as well as undergraduate students and to collaborate fully with other researchers in spatial models. This POWRE project is supported by the MPS Office of Multidisciplinary Activities (OMA).