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Bayesian multi- and matrix-variate modelling: Graphical models and time series

dc.contributor.advisor West, Mike Wang, Hao 2010-05-10T20:17:04Z 2010-05-10T20:17:04Z 2010
dc.description.abstract <p>Modelling and inference with higher-dimensional variables, including studies in multivariate time series analysis, raise challenges to our ability to ``scale-up'' statistical approaches that involve both modelling and computational issues. Modelling issues relate to the interest in parsimony of parametrisation and control over proliferation of parameters; computational issues relate to the basic challenges to the efficiency of statistical computation (simulation and optimisation) with increasingly high-dimensional and structured models. This thesis addresses these questions and explores Bayesian approaches inducing relevant sparsity and structure into parameter spaces, with a particular focus on time series and dynamic modelling.</p> <p>Chapter 1 introduces the challenge of estimating covariance matrices in multivariate time series problems, and reviews Bayesian treatments of Gaussian graphical models that are useful for estimating covariance matrices. Chapter 2 and 3 introduce the development and application of matrix-variate graphical models and time series models. Chapter 4 develops dynamic graphical models for multivariate financial time series. Chapter 5 and 6 propose an integrated approach for dynamic multivariate regression modelling with simultaneous selection of variables and graphical-model structured covariance matrices. Finally, Chapter 7 summarises the dissertation and discusses a number of new and open research directions.</p>
dc.format.extent 27916064 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.subject Statistics
dc.title Bayesian multi- and matrix-variate modelling: Graphical models and time series
dc.type Dissertation
dc.department Statistical Science

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