Bayesian multi- and matrix-variate modelling: Graphical models and time series | Posted on:2011-10-18 | Degree:Ph.D | Type:Thesis | University:Duke University | Candidate:Wang, Hao | Full Text:PDF | GTID:2440390002451383 | Subject:Statistics | Abstract/Summary: | | 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.;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. | Keywords/Search Tags: | Time series, Modelling, Graphical models, Covariance matrices, Chapter, Bayesian, Multivariate | | Related items |
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