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Robust Bayes in Hierarchical Modeling and Empirical Bayes Analysis in Multivariate Estimation
Başlık:
Robust Bayes in Hierarchical Modeling and Empirical Bayes Analysis in Multivariate Estimation
Yazar:
Wang, Xiaomu, author.
ISBN:
9780438097315
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (99 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Berliner L. Mark Committee members: MacEachern Steven; Xu Xinyi.
Özet:
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 epsilon-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.
Notlar:
School code: 0168
Konu Başlığı:
Tüzel Kişi Ek Girişi:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(687194.1) | 687194-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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