The aim of this work is to develop a spatial model for multi-subject fMRI data. While there has been much work on univariate modeling of each voxel for single- and multi-subject data, and some work on spatial modeling for single-subject data, there has been no work on spatial models that explicitly account for intersubject variability in activation location. We use a Bayesian hierarchical spatial model to fit the data. At the first level we model "population centers" that mark the centers of regions of activation. For a given population center each subject may have zero or more associated "individual components". While most previous work uses Gaussian mixtures for the activation shape, we instead use Gaussian mixtures for the probability that a voxel belongs to an activated region, assuming homogeneous mean intensity within a region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov Chain Monte Carlo. We demonstrate our method with a fMRI study of vi- sual working memory and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data.
Xu, Lei; Johnson, Timothy; and Nichols, Thomas, "Bayesian Spatial Modeling of fMRI data: A Multiple-Subject Analysis" (April 2007). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 71.