Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Advancements in Small Area Estimation Using Hierarchical Bayesian Methods and Complex Survey Data(2024) Das, Soumojit; Lahiri, Partha; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation addresses critical gaps in the estimation of multidimensional poverty measures for small areas and proposes innovative hierarchical Bayesian estimation techniques for finite population means in small areas. It also explores specialized applications of these methods for survey response variables with multiple categories. The dissertation presents a comprehensive review of relevant literature and methodologies, highlighting the importance of accurate estimation for evidence-based policymaking. In Chapter \ref{chap:2}, the focus is on the estimation of multidimensional poverty measures for small areas, filling an essential research gap. Using Bayesian methods, the dissertation demonstrates how multidimensional poverty rates and the relative contributions of different dimensions can be estimated for small areas. The proposed approach can be extended to various definitions of multidimensional poverty, including counting or fuzzy set methods. Chapter \ref{chap:3} introduces a novel hierarchical Bayesian estimation procedure for finite population means in small areas, integrating primary survey data with diverse sources, including social media data. The approach incorporates sample weights and factors influencing the outcome variable to reduce sampling informativeness. It demonstrates reduced sensitivity to model misspecifications and diminishes reliance on assumed models, making it versatile for various estimation challenges. In Chapter \ref{chap: 4}, the dissertation explores specialized applications for survey response variables with multiple categories, addressing the impact of biased or informative sampling on assumed models. It proposes methods for accommodating survey weights seamlessly within the modeling and estimation processes, conducting a comparative analysis with Multilevel Regression with Poststratification (MRP). The dissertation concludes by summarizing key findings and contributions from each chapter, emphasizing implications for evidence-based policymaking and outlining future research directions.Item The Bayesian and Approximate Bayesian Methods in Small Area Estimation(2008-11-20) Pramanik, Santanu; Lahiri, Partha; Survey Methodology; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)For small area estimation, model based methods are preferred to the traditional design based methods because of their ability to borrow strength from related sources. The indirect estimates, obtained using mixed models, are usually more reliable than the direct survey estimates. To draw inferences from mixed models, one can use Bayesian or frequentist approach. We consider the Bayesian approach in this dissertation. The Bayesian approach is straightforward. The prior and likelihood produce the posterior, which is used for all inferential purposes. It overcomes some of the shortcomings of the empirical Bayes approach. For example, the posterior variance automatically captures all sources of uncertainties in estimating small area parameters. But this approach requires the specification of a subjective prior on the model parameters. Moreover, in almost all situation, the posterior moments involve multi-dimensional integration and consequently closed form expressions cannot be obtained. To overcome the computational difficulties one needs to apply computer intensive MCMC methods. We apply linear mixed normal models (area level and unit level) to draw inferences for small areas when the variable of interest is continuous. We propose and evaluate a new prior distribution for the variance component. We use Laplace approximation to obtain accurate approximations to the posterior moments. The approximations present the Bayesian methodology in a transparent way, which facilitates the interpretation of the methodology to the data users. Our simulation study shows that the proposed prior yields good frequentist properties for the Bayes estimators relative to some other popular choices. This frequentist validation brings in an objective flavor to the so-called subjective Bayesian approach. The linear mixed models are, usually, not suitable for handling binary or count data, which are often encountered in surveys. To estimate the small area proportions, we propose a binomial-beta hierarchical model. Our formulation allows a regression specification and hence extends the usual exchangeable assumption at the second level. We carefully choose a prior for the shape parameter of the beta density. This new prior helps to avoid the extreme skewness present in the posterior distribution of the model parameters so that the Laplace approximation performs well.