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).
