  Analysis of brain imaging scans is critical to understanding the way the
human brain functions, which can be leveraged to treat injuries and conditions
that affect the quality of life for a significant portion of the human
population. In particular, functional magnetic resonance imaging (fMRI) scans
give detailed data on a living subject at high spatial and temporal
resolutions. Due to the high cost involved in the collection of these scans,
robust methods of analysis are of critical importance in order to produce
meaningful inference. Bayesian methods in particular allow for the inclusion of
expected behavior from prior study into an analysis, increasing the power of
the results while circumventing problems that arise in classical analyses,
including the effects of smoothing results and sensitivity to multiple
comparison testing corrections. Recent development of a surface-based spatial
Bayesian general linear model for cortical surface fMRI (cs-fMRI) data provides
the desired power increase in task fMRI data using stochastic partial
differential equation (SPDE) priors. This model relies on the computational
efficiencies of the integrated nested Laplace approximation (INLA) to perform
powerful analyses that have been validated to outperform classical analyses. In
this article, we develop an exact Bayesian analysis method for the GLM,
employing an expectation-maximization (EM) algorithm to find maximum a
posteriori (MAP) estimates of task-based regressors on cs-fMRI and subcortical
fMRI data while using minimal computational resources. Our proposed method is
compared to the INLA implementation of the Bayesian GLM, as well as a classical
GLM on simulated data. A validation of the method on data from the Human
Connectome Project is also provided.
