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dc.contributor.advisorSingh, Sumeetpal S.
dc.contributor.advisorDawid, A. Philip
dc.contributor.authorYildirim, Sinan
dc.date.accessioned2013-07-10T14:12:45Z
dc.date.available2013-07-10T14:12:45Z
dc.date.issued2013-06-11
dc.identifier.otherPhD.36437
dc.identifier.urihttp://www.dspace.cam.ac.uk/handle/1810/244707
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/244707
dc.description.abstractTime series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random variables involved in the definition of the model. When a time series model is to be fitted to some sequentially observed data, it is essential to decide on the value of the parameter that describes the data best, a procedure generally called parameter estimation. This thesis comprises novel contributions to the methodology on parameter estimation in time series models. Our primary interest is online estimation, although batch estimation is also considered. The developed methods are based on batch and online versions of expectation-maximisation (EM) and gradient ascent, two widely popular algorithms for maximum likelihood estimation (MLE). In the last two decades, the range of statistical models where parameter estimation can be performed has been significantly extended with the development of Monte Carlo methods. We provide contribution to the field in a similar manner, namely by combining EM and gradient ascent algorithms with sequential Monte Carlo (SMC) techniques. The time series models we investigate are widely used in statistical and engineering applications. The original work of this thesis is organised in Chapters 4 to 7. Chapter 4 contains an online EM algorithm using SMC for MLE in changepoint models, which are widely used to model heterogeneity in sequential data. In Chapter 5, we present batch and online EM algorithms using SMC for MLE in linear Gaussian multiple target tracking models. Chapter 6 contains a novel methodology for implementing MLE in a hidden Markov model having intractable probability densities for its observations. Finally, in Chapter 7 we formulate the nonnegative matrix factorisation problem as MLE in a specific hidden Markov model and propose online EM algorithms using SMC to perform MLE.en_GB
dc.language.isoenen_GB
dc.subjectSequential Monte Carloen_GB
dc.subjectParameter estimationen_GB
dc.subjectBayesian statisticsen_GB
dc.titleMaximum likelihood parameter estimation in time series models using sequential Monte Carloen_GB
dc.typeThesisen_GB
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridgeen_GB
dc.publisher.departmentDepartment of Pure Mathematics and Mathematical Statisticsen_GB
dc.publisher.departmentStatistical Laboratoryen_GB
dc.publisher.departmentDarwin Collegeen_GB
dc.identifier.doi10.17863/CAM.16227


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