Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
8-2015
Committee Chair or Co-Chairs
Michele Joyner
Committee Members
Jeff Knisley, Ariel Cintron-Arias
Abstract
Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a new method, the MCR method, which is unique to stochastic models and provides significantly better estimates and smaller confidence intervals for parameter values. Initial analysis of the new MCR method indicates that this method might be a viable method for parameter estimation for continuous time Markov chain models.
Document Type
Thesis - unrestricted
Recommended Citation
Robacker, Thomas C., "Comparison of Two Parameter Estimation Techniques for Stochastic Models" (2015). Electronic Theses and Dissertations. Paper 2567. https://dc.etsu.edu/etd/2567
Copyright
Copyright by the authors.
Included in
Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Applied Mathematics Commons, Statistical Models Commons