Estimating spatiotemporal models for multi-subject fMRI is computationally challenging. We propose a mixed model for localization studies with spatial random effects and time-series errors. We develop method-of-moment estimators that leverage population and spatial information and are scalable to massive datasets. In simulations, subject-specific estimates of activation are considerably more accurate than the standard voxel-wise general linear model. Our mixed model also allows for valid population inference. We apply our model to cortical data from motor and theory of mind tasks from the Human Connectome Project (HCP). The proposed method results in subject-specific predictions that appear smoother and less noisy than those from the popular single-subject univariate approach. In particular, the regions of motor cortex associated with a left-hand finger-tapping task appear to be more clearly delineated. Subject-specific maps of activation from task fMRI are increasingly used in pre-surgical planning for tumor removal and in locating targets for transcranial magnetic stimulation. Our findings suggest that using spatial and population information is a promising avenue for improving clinical neuroimaging
