Jarad B. Niemi
Assistant ProfessorIowa State University
Bayesian Analysis and Computational Methods for Dynamic Modeling
Dynamic models, also termed state-space models, comprise an extremely rich model class for time series analysis. This dissertation focuses on building dynamic models for a variety of contexts and computationally efficient methods for Bayesian inference for simultaneous estimation of latent states and unknown fixed parameters. Chapter 1 introduces dynamic models and methods of inference in these models including standard approaches in Markov chain Monte Carlo and sequential Monte Carlo methods. Chapter 2 describes a novel method for jointly sampling the entire latent state vector in a nonlinear Gaussian dynamic model using a computationally efficient adaptive mixture modeling procedure. This method, termed AM4, is embedded in an overall Markov chain Monte Carlo algorithm for estimating fixed parameters as well as states. In Chapter 3, AM4 is implemented in a few illustrative nonlinear models and compared to standard existing methods. This chapter also looks at the effect of the number of mixture components as well as length of the time series on the efficiency of the method. I then turn to biological applications in Chapter 4. I discuss modeling choices as well as derivation of the dynamic model to be used in this application. Parameter and state estimation are performed for both simulated and real data. Chapter 5 extends the methodology introduced in Chapter 2 from nonlinear Gausiv sian models to general dynamic models. The method is then applied to a financial stochastic volatility model on US $ - British � exchange rates and identifies a limitation in the current state-of-the-art method in that field. Bayesian inference in the previous chapter is accomplished through Markov chain Monte Carlo which is suitable for batch analyses, but computationally limiting in sequential analysis. Chapter 6 introduces sequential Monte Carlo. It discusses two methods currently available for simultaneous sequential estimation of latent states and fixed parameters and then introduces a novel algorithm that reduces the key, limiting degeneracy issue while being usable in a wide model class. This new method is applied to a biological model discussed in Chapter 4. Chapter 7 implements and compares novel sequential Monte Carlo algorithms in the disease surveillance context modeling influenza epidemics. Finally, Chapter 8 suggests areas for future work in both modeling and Bayesian inference. Several appendices provide detailed technical support material as well as relevant related work.