Parallel stochastic particle methods using Markov Chain random walks
Abstract/Contents
- Abstract
- Particle methods, also known as Monte Carlo methods in the statistical community, have become a powerful tool for a variety of research areas such as chemistry, astronomy, and finance, to list a few. This is mainly due to the enormous advances in computational resources in recent years. In this work, we consider an efficient and robust parallel methodology that can be applied to particle methods in a general setting. The parallel methodology proposed in this thesis takes advantage of Markov Chain random walks and corresponding Markov chain theory. We develop parallel stochastic particle methods in two different areas: (1) the optimal filtering problem, and (2) simulation of particle coagulation. In each application, a mathematical proof of convergence as well as a numerical example are provided. After a brief review of Markov Chain random walks and an explanation of the two application areas, the Markov Chain Distributed Particle Filter (MCDPF) algorithm is introduced. The performance of this method is demonstrated with a bearing-only-measurement target-tracking numerical example and is further compared with an existing method, the Distributed Extended Kalman Filter (DEKF), using a flocking model for the target vehicles. We study the convergence of MCDPF to the Centralized Particle Filter (CPF) and the optimal filtering solution by using results from Markov chain theory. In addition, the robustness of the MCDPF method is highlighted for practical problems. As the second application area, we developed a parallel stochastic particle method for the stochastic simulation of Smoluchowski's coagulation equation. This equation is used in many broad areas and for high-dimensional problems the stochastic particle solution is more accurate, stable and computationally cheaper than classical numerical integration schemes. In this application, simulated particles can be considered as representing physical particles. Since more particles result in more accurate and useful solutions, it is desirable to simulate this equation with a greater number of particles. By applying the parallel stochastic particle method, a comparable solution is obtained more efficiently using multiple processors, where one processor maintains many fewer particles by communicating with neighboring processors. A numerical study as well as a theoretical analysis are provided to demonstrate the convergence of the parallel stochastic particle algorithm.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Copyright date | 2011 |
| Publication date | 2010, c2011; 2010 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Lee, Sun Hwan |
|---|---|
| Associated with | Stanford University, Department of Aeronautics and Astronautics |
| Primary advisor | Glynn, Peter W |
| Primary advisor | West, Matthew, 1975- |
| Thesis advisor | Glynn, Peter W |
| Thesis advisor | West, Matthew, 1975- |
| Thesis advisor | Alonso, Juan José, 1968- |
| Thesis advisor | Lall, Sanjay |
| Advisor | Alonso, Juan José, 1968- |
| Advisor | Lall, Sanjay |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Sun Hwan Lee. |
|---|---|
| Note | Submitted to the Department of Aeronautics and Astronautics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2011. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Sun Hwan Lee
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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