Das, SoumojitThis 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.enDissertationStatisticsComplex Survey DataData IntegrationHierarchical BayesModel based methodsSmall Area EstimationSurvey Sampling