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Title: Statistical methods for non-stationary time series analysis
Author: Campbell, N. C.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2000
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This dissertation is concerned with Bayesian methods for non-stationary time series analysis. Most of the algorithms developed use Markov chain Monte Carlo (MCMC) methods as the means of sampling from the required posteriors. A stochastic version of the Expectation Maximisation (EM) algorithm, the Expectation Sample (ES) algorithm is developed. The performance of this algorithm is compared with EM and other stochastic EM algorithms for parameter estimation of locally stationary time series. The ES algorithm is shown to overcome some of the well documented limitations of the EM algorithm. Non-stationary time series are commonly modelled by segmenting them into a number of independent frames that can be considered stationary. An algorithm is developed whereby these individuals segments can be considered to be dependent on each other. This algorithm is used for the task of noise reduction of a long audio signal and it is shown that the new algorithm gives improved results compared to existing techniques. The time-varying Autoregressive (TVAR) model is introduced as a non-stationary time series model. Basis functions are used to model the TVAR coefficients and an MCMC algorithm developed to perform subset selection on the set of chosen basis functions. Results show that this algorithm is capable of reducing the number of basis functions used to model each TVAR coefficient. The subset selection algorithm is extended to deal with the problem of unknown TVAR model order. Two MCMC algorithms are developed; a reversible jump algorithm and a combined subset selection algorithm. An application to noise reduction of audio signals is considered. The techniques developed previously are extended to account for the fact that the signal is now observed in noise. The algorithm is demonstrated using real audio with added white noise.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available