  Neuroradiologists and neurosurgeons increasingly opt to use functional
magnetic resonance imaging (fMRI) to map functionally relevant brain regions
for noninvasive presurgical planning and intraoperative neuronavigation. This
application requires a high degree of spatial accuracy, but the fMRI
signal-to-noise ratio (SNR) decreases as spatial resolution increases. In
practice, fMRI scans can be collected at multiple spatial resolutions, and it
is of interest to make more accurate inference on brain activity by combining
data with different resolutions. To this end, we develop a new Bayesian model
to leverage both better anatomical precision in high resolution fMRI and higher
SNR in standard resolution fMRI. We assign a Gaussian process prior to the mean
intensity function and develop an efficient, scalable posterior computation
algorithm to integrate both sources of data. We draw posterior samples using an
algorithm analogous to Riemann manifold Hamiltonian Monte Carlo in an expanded
parameter space. We illustrate our method in analysis of presurgical fMRI data,
and show in simulation that it infers the mean intensity more accurately than
alternatives that use either the high or standard resolution fMRI data alone.
