  Multi-subject functional magnetic resonance imaging (fMRI) data has been
increasingly used to study the population-wide relationship between human brain
activity and individual biological or behavioral traits. A common method is to
regress the scalar individual response on imaging predictors, known as a
scalar-on-image (SI) regression. Analysis and computation of such massive and
noisy data with complex spatio-temporal correlation structure is challenging.
In this article, motivated by a psychological study on human affective feelings
using fMRI, we propose a joint Ising and Dirichlet Process (Ising-DP) prior
within the framework of Bayesian stochastic search variable selection for
selecting brain voxels in high-dimensional SI regressions. The Ising component
of the prior makes use of the spatial information between voxels, and the DP
component groups the coefficients of the large number of voxels to a small set
of values and thus greatly reduces the posterior computational burden. To
address the phase transition phenomenon of the Ising prior, we propose a new
analytic approach to derive bounds for the hyperparameters, illustrated on 2-
and 3-dimensional lattices. The proposed method is compared with several
alternative methods via simulations, and is applied to the fMRI data collected
from the KLIFF hand-holding experiment.
