A0463
Title: Discrete autoregressive switching processes in sparse graphical modeling of multivariate time series data
Authors: Beniamino Hadj-Amar - University of South Carolina (United States) [presenting]
Aaron Bornstein - University of California Irvine (United States)
Michele Guindani - University of California Los Angeles (United States)
Marina Vannucci - Rice University (United States)
Abstract: A flexible Bayesian approach is proposed for sparse Gaussian graphical modeling of multivariate time series. Temporal correlation is accounted for in the data by assuming that observations are characterized by an underlying and unobserved hidden discrete autoregressive process. Multivariate Gaussian emission distributions are assumed, and spatial dependencies are captured by modeling the state-specific precision matrices via graphical horseshoe priors. The mixing probabilities of the hidden process are characterized via a cumulative shrinkage prior that accommodates zero-inflated parameters for non-active components, and further incorporates a sparsity-inducing Dirichlet prior to estimate the effective number of states from the data. For posterior inference, a sampling procedure is developed that allows estimation of the number of discrete autoregressive lags and the number of states, and that cleverly avoids having to deal with the changing dimensions of the parameter space. Performance of the proposed methodology is thoroughly investigated through several simulation studies. The use of the approach is further illustrated for the estimation of dynamic brain connectivity based on fMRI data collected on a subject performing a task-based experiment on latent learning
