Title: Time Series Analysis for Nonlinear Dynamical Systems with Applications to Modeling of Infectious Diseases
Chair: Associate Professor Ed Ionides
Committee Members: Assistant Professor Yves Atchade, Associate Professor Kerby, Shedden, Assistant Professor Stilian Stoev, Assistant Professor Aaron King (EEB)
Abstract: Estimation of static (or time constant) parameters in a general class of nonlinear, non-Gaussian, partially observed Markovian state space model is an active area of research that has seen an explosion in the last seventeen years since the formulation of the particle filter and sequential Monte Carlo methods. In this dissertation, we focus on a likelihood based estimation technique known as iterated filtering. The key feature of iterated filtering that makes it attractive is we do not need to evaluate the state transition densities in a partially observed Markovian state space model. Instead, we just need to be able to draw samples from those densities, which is typically a lot simpler. This allows great flexibility to the modeler since inference can proceed as long as one is able to write down state transition equations generating trajectories from the model. We discuss some key theoretical properties of iterated filtering. In particular, we prove the consistency of the method and find connections between iterated filtering and well known stochastic approximation methods. We also use the iterated filtering technique to estimate parameters and hence answer scientific questions regarding the effect of climate on malaria transmission in Northwest India. We conclude by suggesting possible improvements to likelihood estimation techniques via sequential Monte Carlo filters in an off-line setting.