  In recent years, Bayesian statistics methods in neuroscience have been
showing important advances. In particular, detection of brain signals for
studying the complexity of the brain is an active area of research. Functional
magnetic resonance imagining (fMRI) is an important tool to determine which
parts of the brain are activated by different types of physical behavior.
According to recent results there is evidence that the values of the
connectivity brain signal parameters are close to zero and due to the nature of
time series fMRI data with high frequency behavior, Bayesian dynamic models for
identifying sparsity are indeed far-reaching. We propose a multivariate
Bayesian dynamic approach for model selection and shrinkage estimation of the
connectivity parameters. We describe the coupling or lead-lag between any pair
of regions by using mixture priors for the connectivity parameters and propose
a new weakly informative default prior for the state variances. This framework
produces one-step-ahead proper posterior predictive results and induces
shrinkage and robustness suitable for fMRI data in the presence of sparsity. To
explore the performance of the proposed methodology we present simulation
studies and an application to functional magnetic resonance imaging data.
