  Task-evoked functional magnetic resonance imaging studies, such as the Human
Connectome Project (HCP), are a powerful tool for exploring how brain activity
is influenced by cognitive tasks like memory retention, decision-making, and
language processing. A fast Bayesian function-on-scalar model is proposed for
estimating population-level activation maps linked to the working memory task.
The model is based on the canonical polyadic (CP) tensor decomposition of
coefficient maps obtained for each subject. This decomposition effectively
yields a tensor basis capable of extracting both common features and
subject-specific features from the coefficient maps. These subject-specific
features, in turn, are modeled as a function of covariates of interest using a
Bayesian model that accounts for the correlation of the CP-extracted features.
The dimensionality reduction achieved with the tensor basis allows for a fast
MCMC estimation of population-level activation maps. This model is applied to
one hundred unrelated subjects from the HCP dataset, yielding significant
insights into brain signatures associated with working memory.
