Parameter Estimation for Nonlinear State Space Models
This thesis explores the methodology of state, and in particular, parameter estimation for time series datasets. Various approaches are investigated that are suitable for nonlinear models and non-Gaussian observations using state space models. The methodologies are applied to a dataset consisting of the historical lynx and hare populations, typically modeled by the Lotka- Volterra equations. With this model and the observed dataset, particle filtering and parameter estimation methods are implemented as a way to better predict the state of the system. Methods for parameter estimation considered include: maximum likelihood estimation, state augmented particle filtering, multiple iterative filtering and particle Markov chain Monte Carlo (PMCMC) methods. The specific advantages and disadvantages for each technique are discussed. However, in most cases, PMCMC is the preferred parameter estimation solution. It has the advantage over other approaches in that it can well approximate any posterior distribution from which inference can be made.