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Abstract:
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Brain effective connectivity investigates the directed influence of one region over different regions of the human brain. In this talk, In this paper, we propose a computationally efficient time-varying Bayesian VAR approach for modeling high-dimensional time series. More specifically, we assume a tensor decomposition for the VAR coefficient matrices at different lags. Moreover, we capture dynamically varying connectivity patterns by assuming that at any given time the VAR coefficient matrices are obtained as a mixture of only an active subset of components in the tensor decomposition. A Ising prior is used to select components over time. We employ a multi-way Dirichlet generalized double Pareto prior to allow for global-local shrinkage of the coefficients and to determine automatically the rank of the tensor decomposition. We further assume an increasing-shrinkage prior to guide the selection of the lags of the auto-regression. The proposed prior structure encourages sparsity in the tensor structure and allows to ascertain model complexity through the posterior distribution. We apply our model on a simulation study as well as real fMRI data application.
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