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Title: Bayesian inference via MCMC methods with applications in non-linear time series
Author: Amiri, E.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 1997
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In Bayesian studies there are two main approaches, namely Bayesian inference and Bayesian decision theory. In this thesis Bayesian inference, which is based on summaries of posterior information, is targeted. In order to get posterior information, a Bayesian is usually confronted with awkward integrals. There are different solutions in the literature for evaluating these integrals. When these solutions fail to work Markov chain Monte Carlo (MCMC) methods are reasonable alternatives. The aim of this thesis is twofold. First is the review of the literature on MCMC methods for general purpose applications and second application of these methods to nonlinear time series modeling. In the first instance, different aspects of MCMC methods together with examination of their credibility are reviewed. The Gibbs sampler and the Metropolis-Hastings algorithms are among the important MCMC algorithms. A random visitation Gibbs sampler is proposed for multivariate Gaussian distributions and a simulating annealing method based on fractional powers is introduced. Convergence of MCMC is a main issue. Ritter and Tanner's convergence diagnostic method has been modified to render it applicable to the Metropolis Hastings algorithm. For a second part, SETAR models are chosen as an application and studies are conducted within a Bayesian framework. Applications within this area are many. We begin by introducing several criteria for model choice and scrutinizing their applicability. Then forecasting procedures are developed and sensitivity analysis is conducted. Automatic identification of the delay, thresholds and maximum orders by random generation from their joint posterior distribution is performed. Finally, lag selection in regimes is carried out by introducing an auxiliary binary variable.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available