  In this work, we propose a modeling procedure for fMRI data analysis using a
Bayesian Matrix-Variate Dynamic Linear Model (MVDLM). With this type of model,
less complex than the more traditional temporal-spatial models, we are able to
take into account the temporal and -- at least locally -- the spatial
structures that are usually present in this type of data. Despite employing a
voxel-wise approach, every voxel in the brain is jointly modeled with its
nearest neighbors, which are defined through a euclidian metric. MVDLM's have
been widely used in applications where the interest lies in to perform
predictions and/or analysis of covariance structures among time series. In this
context, our interest is rather to assess the dynamic effects which are related
to voxel activation. In order to do so, we develop three algorithms to simulate
online-trajectories related to the state parameter and with those curves or
simulated trajectories we compute a Monte Carlo evidence for voxel activation.
Through two practical examples and two different types of assessments, we show
that our method can be viewed for the practitioners as a reliable tool for fMRI
data analysis. Despite all the examples and analysis are illustrated just for a
single subject analysis, we also describe how more general group analysis can
be implemented.
