  Functional magnetic resonance imaging or functional MRI (fMRI) is a
non-invasive way to assess brain activity by detecting changes associated with
blood flow. In this work, we propose a full Bayesian procedure to analyze fMRI
data for individual and group stages. For the individual stage we use a
multivariate dynamic linear model (MDLM), where the temporal dependence is
modeled through the state parameters and the spatial dependence is modeled only
locally, taking the nearest neighbors of each voxel location. For the group
stage we take advantage of the posterior distribution of the state parameters
obtained in the individual stage and create a new posterior distribution that
represents the updated beliefs for the group analysis. Since the posterior
distribution for the state parameters is indexed by the time $t$, we propose an
algorithm that allows on-line estimated curves of the state parameters to be
drawn and posterior probabilities computed in order to assess brain activation
for both individual and group analysis. We propose an alternative analysis for
the group stage using a Gaussian process ANOVA model, where the on-line
estimated curves obtained in the individual stage are modeled as a functional
response. Finally, we assess our proposed modeling procedure using real
resting-state data and computing empirical false-positive brain activation
rates.
