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The Ohio State University

1. Sengupta, Aritra. Empirical Hierarchical Modeling and Predictive Inference for Big, Spatial, Discrete, and Continuous Data.

Degree: PhD, Statistics, 2012, The Ohio State University

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 model (e.g., Chapter 2), and through data-model specifications (e.g., Chapter 3). Following the introductory chapter, in Chapter 2 we consider spatial data in the form of counts. We consider a Poisson data model for the counts, and develop maximum likelihood (ML) estimates for the unknown parameters using an expectation-maximization (EM) algorithm. We illustrate the hierarchical nature of our approach to the spatial modeling of counts, through the analysis of a spatial dataset of Sudden Infant Death Syndrome (SIDS) counts for the counties of North Carolina. Then, in Chapter 3, we extend the empirical hierarchical modeling framework of Chapter 2, which was developed for counts, to the exponential family of distributions. The data model is a conditionally independent exponential-family model. A process model is specified for some transformation of the (conditional) mean of the data model. We present the EM algorithm to obtain ML estimates of the unknown parameters in the empirical-hierarchical-modeling framework introduced in… Advisors/Committee Members: Cressie, Noel (Advisor).

Subjects/Keywords: Statistics; Aerosol optical depth; EM algorithm; empirical Bayes; geostatistical process; Laplace approximation; massive dataset; maximum likelihood estimation; MCMC; MODIS instrument; optimal spatial prediction; SRE model

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APA (6th Edition):

Sengupta, A. (2012). Empirical Hierarchical Modeling and Predictive Inference for Big, Spatial, Discrete, and Continuous Data. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1350660056

Chicago Manual of Style (16th Edition):

Sengupta, Aritra. “Empirical Hierarchical Modeling and Predictive Inference for Big, Spatial, Discrete, and Continuous Data.” 2012. Doctoral Dissertation, The Ohio State University. Accessed October 20, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1350660056.

MLA Handbook (7th Edition):

Sengupta, Aritra. “Empirical Hierarchical Modeling and Predictive Inference for Big, Spatial, Discrete, and Continuous Data.” 2012. Web. 20 Oct 2019.

Vancouver:

Sengupta A. Empirical Hierarchical Modeling and Predictive Inference for Big, Spatial, Discrete, and Continuous Data. [Internet] [Doctoral dissertation]. The Ohio State University; 2012. [cited 2019 Oct 20]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1350660056.

Council of Science Editors:

Sengupta A. Empirical Hierarchical Modeling and Predictive Inference for Big, Spatial, Discrete, and Continuous Data. [Doctoral Dissertation]. The Ohio State University; 2012. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1350660056

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