Doctor of Philosophy, The Ohio State University, 2012, Statistics
This dissertation is comprised of an introductory chapter and three stand-alone chapters. The three main chapters are tied together by a common theme: empirical hierarchical spatial-statistical modeling of non-Gaussian datasets. Such non-Gaussian datasets arise in a variety of disciplines, for example, in health studies, econometrics, ecological studies, and remote sensing of the Earth by satellites, and they are often very-large-to-massive. When analyzing ``big data,'' traditional spatial statistical methods are computationally intensive and sometimes not feasible, even in supercomputing environments. In addition, these datasets are often observed over extensive spatial domains, which make the assumption of spatial stationarity unrealistic.
In this dissertation, we address these issues by using dimension-reduction techniques based on the Spatial Random Effects (SRE) model. We consider a hierarchical spatial statistical model consisting of a conditional exponential-family model for the observed data (which we call the data model), and an underlying (hidden) geostatistical process for some transformation of the (conditional) mean of the data model. Within the hierarchical model, dimension reduction is achieved by modeling the geostatistical process as a linear combination of a fixed number of basis functions, which results in substantial computational speed-ups. These models do not rely on specifying a spatial weights matrix, and no assumptions of homogeneity, stationarity, or isotropy are made.
Another focus of the research presented in this dissertation is to properly account for spatial heterogeneity that often exists in these datasets. For example, with county-level health data, the population at risk is different for different counties and is typically a source of heterogeneity. This type of heterogeneity, whenever it exists, needs to be incorporated into the hierarchical model. We address this through the use of an offset term and by properly weighting the SRE (open full item for complete abstract)
Committee: Noel Cressie PhD (Advisor); Radu Herbei PhD (Committee Member); Desheng Liu PhD (Committee Member)
Subjects: Statistics