Some analyses of markov chains by the coupling method
Abstract/Contents
- Abstract
- This thesis is concerned with the non-asymptotic convergence rates of various Markov chains, and consists of two main sections. In the first section, I investigate the properties of random birth and death chains with fixed stationary distributions. The main results include a proof of the fact that random birth and death chains are in some sense less likely to exhibit cutoff than a certain natural family of birth and death chains, and conversely a proof that several natural families of random birth and death chains do exhibit cutoff. In the second section, I find accurate bounds for the convergence of Gibbs samplers on continuous state spaces. This includes a resolution of Aldous' conjecture on the mixing time of a sampler on the unit simplex, a generalization of work by Randall and Winkler on a related Gibbs sampler associated to a graph, and improvements on existing bounds on the convergence rates of Kac's walk on the sphere and a Gibbs sampler on narrow matrices with fixed row and column sums.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Smith, Aaron Matthew |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Diaconis, Persi |
| Thesis advisor | Diaconis, Persi |
| Thesis advisor | Dembo, Amir |
| Thesis advisor | Soundararajan, Kannan, 1973- |
| Advisor | Dembo, Amir |
| Advisor | Soundararajan, Kannan, 1973- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Aaron Smith. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Aaron Matthew Smith
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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