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BAYESIAN MODELS FOR LARGE-DIMENSIONAL TIME SERIES Raquel Prado Department of Applied Mathematics and Statistics University of California Santa Cruz, USA This short course will present approaches for modeling large-dimensional and non-stationary time series data that arise in a variety of applied fields, including biomedical signal processing, environmental sciences and finance. We will begin with an introduction to Bayesian modeling of stationary and non-stationary time series that focuses on state-space representations and inference for ARMA models, time-varying autoregressive models, decompositions for non-stationary time series, and latent autoregressive models. Connections with spectral-domain approaches will be explored. We will then consider more general state-space representations for large-dimensional multivariate time series such as factor models with structured latent factors and mixtures of dynamic models. Computational methods for inference within these classes of models, including Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods, will be studied. The course will highlight the application of these statistical models and computational methods to the analysis of large-dimensional neuroscience data such as fMRI and EEG.
Lecture 1: Motivation: Analysis of large-dimensional brain signals. Modeling and computational challenges in the analysis of neuroscience data. Bayesian models for stationary time series: Autoregressions and ARMA models with structured priors. Time series decompositions and spectral approaches.
Lecture 2: Bayesian state-space models for non-stationary time series. Review of dynamic linear models. Time-varying autoregressions. Computation and examples. Case study: Analysis of multi-channel electroencephalogram data.
Lecture 3: More general state-space models. Hierarchical models. MCMC inference. Dynamic factor models. Case studies: Discovering latent structure in EEG and fMRI data. Lecture 4: Sequential Monte Carlo in dynamic models. State-space autoregressions with structured priors. Real time parameter learning and filtering in state-space autoregressions.
Lecture 5: Mixtures in dynamic models. Multi-process models. Stochastic volatility models. Mixtures of structured autoregressions. Approximate Bayesian inference and SMC methods. Examples.
Lecture 6: Additional multivariate and matrix-variate dynamic models. VAR and TV-VAR models. Examples. Extensions and future directions.
Textbook The main support text for the course is the book: Time Series: Modeling, Computation, and Inference (2010) by R. Prado and M. West published by Chapman and Hall/CRC Press.
March 6, 2014
Bayesian Models for Large-Dimensional Time Series, Bocconi 2014