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Robust Bayes in Hierarchical Modeling and Empirical Bayes Analysis in Multivariate Estimation

Wang, Xiaomu
http://orcid.org/0000-0003-2016-7513
http://rave.ohiolink.edu/etdc/view?acc_num=osu1449069220

Abstract Details

2015, Doctor of Philosophy, Ohio State University, Statistics.
With the modern development of statistical data analysis, the data volume increases and the data dimension increases correspondingly. This thesis investigates two classic Bayes problems: robust Bayes analysis in hierarchical modeling and empirical Bayes analysis in multivariate estimation. Our goals are to provide approaches in high-dimensional settings. In Bayesian analysis, it is difficult to develop a single prior to completely and fully quantify our prior information. Thereby, o-contamination classes have become popular models of the uncertainty in prior distributions. For the first part of the thesis, I focus on investigating the posterior ranges for different o-contamination classes for hyper-parameters in the context of hierarchical Bayesian modeling. We derive posterior ranges under various interesting settings and examples. When a class of priors is assumed in Bayesian analysis, it is vital to consider a decision rule corresponding to this class. In a multivariate estimation setting, for the second part of this thesis, I focus on research to find a compromise between single James-Stein (JS) estimator and separated JS estimators. Then we investigate the risk of such estimators with different numerical simulations and compare the results with JS rules.
Berliner L. Mark (Advisor)
MacEachern Steven (Committee Member)
Xu Xinyi (Committee Member)
98 p.
Statistics
robust Bayes, multivariate estimation, empirical Bayes, James-Stein, hierarchical model

Recommended Citations

Citations

  • Wang, X. (2015). Robust Bayes in Hierarchical Modeling and Empirical Bayes Analysis in Multivariate Estimation [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1449069220

    APA Style (7th edition)

  • Wang, Xiaomu. Robust Bayes in Hierarchical Modeling and Empirical Bayes Analysis in Multivariate Estimation. 2015. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1449069220.

    MLA Style (8th edition)

  • Wang, Xiaomu. "Robust Bayes in Hierarchical Modeling and Empirical Bayes Analysis in Multivariate Estimation." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1449069220

    Chicago Manual of Style (17th edition)

osu1449069220
83,028
© 2015, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.