The aim of this work is to develop a spatial semiparametric Bayesian 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 virtually no work on spatial models that explicitly account for inter-subject variability in activation location. The data are fitted with a Bayesian semiparametric hierarchical spatial model. While most previous work uses Gaussian mixtures for the activation shape, at the first level we instead use Gaussian mixtures for the probability that a voxel belongs to an activated region. Spatial correlation is accounted for in the mixing weights. At the second level mixture component means are clustered about individual activation centers. At the third level individual activation centers are clustered about population centers. At the fourth level, population parameters are modeled as a Dirichlet process. Our approach incorporates the unknown number of mixture components and individual centers into the model as parameters whose posterior distributions are estimated by reversible jump Markov Chain Monte Carlo (RJMCMC) at levels two and three. A mixture of Dirichlet process priors (MDP) is used to nonparametrically model the distribution of individual centers about the population centers at level 4. We demonstrate our method with an fMRI study of resolving proactive interference.
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