Combining Images Across Multiple Subjects

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This article introduces a Bayesian hierarchical model for combining information across multiple images. Our work was motivated by an invasive functional brain mapping technique called direct cortical electrical interference that gives a sparse set of binary observations of an underlying “true” region at multiple sites on the brain surface. To model region shapes that may vary widely across individuals, we use mixtures of simple templates, for example, circles. These subject-specific templates are treated as random effects, governed by a set of population templates that make up a population region. The numbers of subject-specific and population templates are treated as unknown variables to be estimated from the data. Conditional on the subject-specific regions, the observed data are modeled using logistic regression. To estimate the variability among images across patients, we develop a measure based on Baddeley's error measure for binary images. Because the dimension of the parameter space changes as the numbers of subject-specific and population templates change, inference is made using reversible jump Markov chain Monte Carlo. Using a hierarchical approach, we may better estimate each individual's region by borrowing strength from other subjects' data, we can estimate a population region by pooling information across subjects, and we can use a collection of data from previous patients to predict the location of a future patient's region of interest. The approach is illustrated with DCEI data collected on 20 patients for two motor tasks: tongue and hand movements.