Abstract: This dissertation introduces new classes of models and approaches to multivariate time series analysis and forecasting, with a focus on various problems in which time series structure is driven by underlying latent processes of key interest. The identi- cation of latent structure and common features in multiple time series is rst studied using wavelet based methods and Bayesian time series decompositions of certain classes of dynamic linear models. The results are applied to turbulence and geochemical time series data, the latter involving development of new time series models for latent time-varying autoregressions with heavy-tailed components for quite radically ill-behaved series. Natural extensions and generalizations of these models lead to novel developments of two key model classes, dynamic factor models for multivariate nancial time series with stochastic volatility components, and multivariate dynamic generalized linear models for non-Gaussian longitudinal time series. These two model classes are related through common statistical structure, and the dissertation discusses issues of Bayesian model specication, model tting and computation for posterior and predictive analysis that are common to the two model classes. Two motivating applications are discussed, one in each of the two model classes. The rst concerns short term forecasting and dynamic portfolio allocation, illustrated in a study of the dynamic factor structure of daily spot exchange rates for a selection of international currencies. The second application involves analyses of time series of collections of many related binomial outcomes and arises in a project in health care quality monitoring with the Veterans Aairs (VA) hospital system.

Abstract: This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional measurements are available, for example, gene expression data produced by microarray techniques. For computational or other reasons, people may select only a small subset of features when modelling such data, by looking at how relevant the features are to predicting the response, based on some measure such as correlation with the response in the training data. Although it is used very commonly, this procedure will make the response appear more predictable than it actually is. In Chapter 2, we propose a Bayesian method to avoid this selection bias, with application to naive Bayes models and mixture models. High dimensional features also arise when we consider high-order interactions. The num- ber of parameters will increase exponentially with the order considered. In Chapter 3, we propose a method for compressing a group of parameters into a single one, by exploiting the fact that many predictor variables derived from high-order interactions have the same values for all the training cases. The number of compressed parameters may have converged before considering the highest possible order. We apply this compression method to logistic sequence prediction models and logistic classification models. We use both simulated data and real data to test our methods in both chapters.