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. / Statistics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/2865 |
| Date | January 2019 |
| Creators | Fletcher, Douglas |
| Contributors | Mukhopadhyay, Subhadeep, Izenman, Alan Julian, Wei, William W. S., Hickman, Randal, Obeid, Iyad, 1975- |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 159 pages |
| 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., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/2847, Theses and Dissertations |
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