We present new statistical methodology addressing problems in functional magnetic resonance imaging (fMRI) and climatology. Functional neuroimaging studies present a number of challenges in capturing variability across subjects and across regions of the brain. We present two new methods for analyzing fMRI studies which address these challenges. First, we propose a exible approach for modeling and spa- tially clustering functional response curves for multi-subject fMRI data. Our goal is to segment the brain into regions with similar response curves over levels of a stimulus, and to estimate these region-wide curves and their variability at the levels of sub- jects and of spatial locations. We apply functional data analytic modeling techniques to response functions to model differences across subjects and across space, and em- ploy a model-based unsupervised spatial clustering algorithm to estimate regions with homogeneous response proles. Second, we propose a technique for estimating popu- lation distributions of the onset and duration of brain activation using change point detection methods. We explicitly model each subjects onset and duration as ran- dom variables drawn from unknown distributions. These distributions are estimated assuming no functional form, along with the probability of activation at each time point. Finally, we address the problem of detecting change points in the covariance structure of multivariate climate time series, with application to the relationship be- tween the El Nino southern oscillation and monsoon rainfall in India and Brazil. We present a parametric test for retrospective detection of change points in covariance matrices, along with a variation designed to increase power under multiple change point alternatives.
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