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Trace Class Markov Chains for Bayesian Shrinkage Models
Başlık:
Trace Class Markov Chains for Bayesian Shrinkage Models
Yazar:
Zhang, Liyuan, author.
ISBN:
9780438122383
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (111 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Kshitij Khare.
Özet:
High-dimensional data, where the number of variables exceeds or is comparable to the sample size, is now pervasive in many scientific applications. In recent years, Bayesian shrinkage models have been developed as effective and computationally feasible tools to analyze such data, especially in the context of linear regression. In the dissertation, we focus on the Bayesian lasso model developed by Park & Casella (2008) and generalized version---the Normal-Gamma model developed by Griffin & Brown (2010) and Dirichlet-Laplace model developed by Bhattacharya et al. (2013). For all three models, a three-block Gibbs sampling algorithm to sample from the resulting intractable posterior distribution has been developed. We develop an alternative two-block Gibbs sampling algorithm for each model, and rigorously demonstrate its advantage over the three-block sampler by comparing specific spectral properties. In particular, we show that the Markov operator corresponding to the two-block sampler is trace class (and hence Hilbert-Schmidt), whereas the operator corresponding to the three-block sampler is not even Hilbert-Schmidt. The trace class property for the two-block sampler implies geometric convergence for the associated Markov chain, which justifies the use of Markov chain CLT's to obtain practical error bounds for MCMC based estimates. Additionally, it facilitates theoretical comparisons of the two-block sampler with sandwich algorithms which aim to improve performance by inserting inexpensive extra steps in between the two conditional draws of the two-block sampler.
Notlar:
School code: 0070
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(696667.1) | 696667-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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