Consistency and convergence rate of Markov chain quasi Monte Carlo with examples
Abstract/Contents
- Abstract
- Markov Chain Monte Carlo methods have been widely used in various scientific disciplines for generation of samples from distributions that are difficult to simulate directly. The random numbers driving Markov Chain Monte Carlo algorithms are modeled as independent $\mathcal{U}[0,1)$ random variables. The class of distributions that could be simulated are largely broadened by using Markov Chain Monte Carlo. Quasi-Monte Carlo, on the other hand, aims to improve the accuracy of estimation of an integral over the multidimensional unit cube. By using more carefully balanced inputs, under some smoothness conditions the estimation error is converging at a higher rate than plain Monte Carlo. We would like to combine these two techniques, so that we can sample more accurately from a larger class of distributions. This method, called Markov Chain quasi-Monte Carlo (MCQMC), is the main topic of this work. We are going to replace the IID driving sequence used in MCMC algorithms by a deterministic sequence which is designed to be more uniform. Previously the justification for MCQMC is proved only for finite state space case. We are going to extend those results to some Markov Chains on continuous state spaces. We also explore the convergence rate of MCQMC under stronger assumptions. Lastly we present some numerical results for demonstration of MCQMC's performance. From these examples, the empirical benefits of more balanced sequences are significant.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2001 [i.e. 2011]; 2011 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Chen, Su |
|---|---|
| Associated with | Stanford University, Department of Statistics |
| Primary advisor | Owen, Art B |
| Thesis advisor | Owen, Art B |
| Thesis advisor | Lai, T. L |
| Thesis advisor | Wong, Wing Hung |
| Advisor | Lai, T. L |
| Advisor | Wong, Wing Hung |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Su Chen. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2011. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Su Chen
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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