dc.contributor.advisor Mukhopadhyay, Subhadeep dc.creator Fletcher, Douglas dc.date.accessioned 2020-11-04T15:19:41Z dc.date.available 2020-11-04T15:19:41Z dc.date.issued 2019 dc.identifier.uri http://hdl.handle.net/20.500.12613/2865 dc.description.abstract The two key issues of modern Bayesian statistics are: (i) establishing a principled approach for \textit{distilling} a statistical prior distribution that is \textit{consistent} with the given data from an initial believable scientific prior; and (ii) development of a \textit{consolidated} Bayes-frequentist data analysis workflow that is more effective than either of the two separately. In this thesis, we propose generalized empirical Bayes as a new framework for exploring these fundamental questions along with a wide range of applications spanning fields as diverse as clinical trials, metrology, insurance, medicine, and ecology. Our research marks a significant step towards bridging the gap'' between Bayesian and frequentist schools of thought that has plagued statisticians for over 250 years. Chapters 1 and 2---based on \cite{mukhopadhyay2018generalized}---introduces the core theory and methods of our proposed generalized empirical Bayes (gEB) framework that solves a long-standing puzzle of modern Bayes, originally posed by Herbert Robbins (1980). One of the main contributions of this research is to introduce and study a new class of nonparametric priors ${\rm DS}(G, m)$ that allows exploratory Bayesian modeling. However, at a practical level, major practical advantages of our proposal are: (i) computational ease (it does not require Markov chain Monte Carlo (MCMC), variational methods, or any other sophisticated computational techniques); (ii) simplicity and interpretability of the underlying theoretical framework which is general enough to include almost all commonly encountered models; and (iii) easy integration with mainframe Bayesian analysis that makes it readily applicable to a wide range of problems. Connections with other Bayesian cultures are also presented in the chapter. Chapter 3 deals with the topic of measurement uncertainty from a new angle by introducing the foundation of nonparametric meta-analysis. We have applied the proposed methodology to real data examples from astronomy, physics, and medical disciplines. Chapter 4 discusses some further extensions and application of our theory to distributed big data modeling and the missing species problem. The dissertation concludes by highlighting two important areas of future work: a full Bayesian implementation workflow and potential applications in cybersecurity. dc.format.extent 159 pages dc.language.iso eng dc.publisher Temple University. Libraries dc.relation.ispartof Theses and Dissertations dc.rights IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available. dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ dc.subject Statistics dc.subject Bayes-frequentist Workflow dc.subject Distributed Learning dc.subject Multidisciplinary Sciences dc.subject Nonparametric Exploratory Modeling dc.subject Uncertainty Modeling dc.title Generalized Empirical Bayes: Theory, Methodology, and Applications dc.type Text dc.type.genre Thesis/Dissertation dc.contributor.committeemember Izenman, Alan Julian dc.contributor.committeemember Wei, William W. S. dc.contributor.committeemember Hickman, Randal dc.contributor.committeemember Obeid, Iyad dc.description.department Statistics dc.relation.doi http://dx.doi.org/10.34944/dspace/2847 dc.ada.note For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu dc.description.degree Ph.D. refterms.dateFOA 2020-11-04T15:19:41Z
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