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dc.contributor.advisor West, Mike en_US
dc.contributor.author Niemi, Jarad en_US
dc.date.accessioned 2009-05-01T18:29:41Z
dc.date.available 2009-05-01T18:29:41Z
dc.date.issued 2009 en_US
dc.identifier.uri http://hdl.handle.net/10161/1137
dc.description Dissertation en_US
dc.description.abstract <p>Dynamic models, also termed state space models, comprise an extremely rich model class for time series analysis. This dissertation focuses on building state space models for a variety of contexts and computationally efficient methods for Bayesian inference for simultaneous estimation of latent states and unknown fixed parameters.</p><p>Chapter 1 introduces state space models and methods of inference in these models. Chapter 2 describes a novel method for jointly sampling the entire latent state vector in a nonlinear Gaussian state space model using a computationally efficient adaptive mixture modeling procedure. This method is embedded in an overall Markov chain Monte Carlo algorithm for estimating fixed parameters as well as states. In Chapter 3 the method of the previous chapter is implemented in a few illustrative</p><p>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 an biological application in Chapter 4. I discuss modeling choices as well as derivation of the state space model to be used in this application. Parameter and state estimation are analyzed in these models for both simulated and real data. Chapter 5 extends the methodology introduced in Chapter 2 from nonlinear Gaussian models to general state space models. The method is then applied to a financial</p><p>stochastic volatility model on US $ - British £ exchange rates. 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. Chapter 7 implements the novel algorithm in a 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.</p> en_US
dc.format.extent 2993798 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.subject Statistics en_US
dc.subject Biology, Molecular en_US
dc.subject Engineering, Biomedical en_US
dc.subject Bayesian statistics en_US
dc.subject Dynamic models en_US
dc.subject Markov chain Monte Carlo en_US
dc.subject Sequential Monte Carlo en_US
dc.subject State en_US
dc.subject space models en_US
dc.subject Systems biology en_US
dc.title Bayesian Analysis and Computational Methods for Dynamic Modeling en_US
dc.type Dissertation en_US
dc.department Statistical Science en_US

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