||<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>