  In contemporary neuroscience, a key area of interest is dynamic effective
connectivity, which is crucial for understanding the dynamic interactions and
causal relationships between different brain regions. Dynamic effective
connectivity can provide insights into how brain network interactions are
altered in neurological disorders such as dyslexia. Time-varying vector
autoregressive (TV-VAR) models have been employed to draw inferences for this
purpose. However, their significant computational requirements pose challenges,
since the number of parameters to be estimated increases quadratically with the
number of time series. In this paper, we propose a computationally efficient
Bayesian time-varying VAR approach. For dealing with large-dimensional time
series, the proposed framework employs a tensor decomposition for the VAR
coefficient matrices at different lags. Dynamically varying connectivity
patterns are captured by assuming that at any given time only a subset of
components in the tensor decomposition is active. Latent binary time series
select the active components at each time via an innovative and parsimonious
Ising model in the time-domain. Furthermore, we propose parsity-inducing priors
to achieve global-local shrinkage of the VAR coefficients, determine
automatically the rank of the tensor decomposition and guide the selection of
the lags of the auto-regression. We show the performances of our model
formulation via simulation studies and data from a real fMRI study involving a
book reading experiment.
