Description
Accurate parameter estimation in systems of ODEs can be critical to a scientific analysis due to the often physical interpretation of parameters. Historically, researchers have mainly built models incorporating the effects of amplitude variation --- the differing magnitude of responses at any given point in time that is typically modeled as additive iid Gaussian error --- on parameter estimates. What does not appear to be implemented yet is a model incorporating the effects of phase variation --- the differing points in time where features of a process occur --- as well. I present a Bayesian hierarchical model to address this objective in which a key focus is the improved performance of using Hamiltonian Monte Carlo (HMC) to estimate the posterior distribution. Both simulated and experimentally gathered data are used to demonstrate the performance of the model and consequences of ignoring phase variation. Lastly, I conduct studies on the asymptotic performance of a parameter estimator within a frequency framework.
Details
Contributors
- Cheng, Henrique (Author)
- Fricks, John (Thesis advisor)
- Cheng, Dan (Thesis advisor)
- Kao, Ming-Hung (Committee member)
- Motsch, Sebastien (Committee member)
- Lan, Shiwei (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2024
Topical Subject
Resource Type
Language
- eng
Note
- Partial requirement for: Ph.D., Arizona State University, 2024
- Field of study: Statistics
Additional Information
English
Extent
- 213 pages