Bayesian Time Series and Dynamic Models

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Bayesian Time Series and Dynamic Models Mike West Abstract This research involves development of new statistical models, methods and computational algorithms for analysis and forecasting of time series. The investigations will include various aspects of Bayesian state-space modelling for time series, introducing new models for non-stationary time series models, methodology for structured latent process analysis and time series decompositions, new models and computational methods for multiple time series analysis including dynamic latent factor models, dynamic Bayesian hierarchical models, and non-Gaussian and non-linear models. Part of the research involves investigation of strategies for dealing with high-dimensional time series data sets and issues of time series data reduction and summary. Stochastic simulation and computer algorithms are ingredients, and will lead to new computational tools for simulation-based Bayesian analyses in various problems of dynamic modelling and time series analysis. Related areas of the research will include time series model uncertainty, assessment and prior specifications, problems of contamination structures and data cleaning, and models involving statistical mixture structure. These projects represent advances in time series modelling and analysis, and contributions to other areas of statistical science, that will be of broad interest and practical relevance to scientists and researchers in various disciplines as well as to statisticians. The new statistical methods resulting from this project extend the scope of applicability of current time series analysis tools to more complex, non-linear and multivariate problems. A significant component of the research involves computationally intensive methods to fit and explore models to data in applications. The research is motivated, in part, by existing problems of statistical modelling and inference in current application areas in several fields, specifically inclu ding projects in the neurosciences, in geology driven by issues of global environmental change, in financial modelling and forecasting, and in biomedical engineering and signal processing.