| Summary: | <p>Recent developments in data sharing and availability provide a vast new window of opportunity for large-sample fMRI analysis. The increased statistical power resulting from larger sample sizes allows researchers to model previously inaccessible phenomena such as the complex grouping structures present in large multi-level datasets (e.g. genetic, familial, geographical) and the spatial variation present in shape, size and locale of excursion sets (identified regions of activation). This thesis is comprised of two halves, which investigate each of these features in turn.</p>
<p>In the first half, we employ the Linear Mixed Model (LMM) to detect and account for grouping and covariance structure present in large experimental designs. At present, the existing fMRI LMM tools are neither scalable nor fully exploit the computational speed-ups afforded by vectorisation of operations over voxels. For this reason, such tools cannot be employed in the large-sample setting. To address this issue, we derive new expressions for LMM estimation and inference and illustrate their usage to perform computationally efficient large-scale fMRI LMM analyses. Our methods are validated empirically via simulations and illustrated using data drawn from the UK Biobank (Allen et al. 2012).</p>
<p>In the second half, we extend a method proposed by Sommerfeld et al. (2018) to provide confidence bounds for the intersection or ‘conjunction’ of excursion sets that have been acquired across the same spatial region but under different study conditions. Such 'conjunctions’ are of natural interest as they correspond to the question “Where was activation observed under all study conditions?". Our method provides, with a desired confidence, sub- and super-sets of the 'conjunction set' without any assumptions on the dependence between the different conditions. Extensive simulations are provided assessing the method’s performance, and a demonstration of the method is given using data drawn from the Human Connectome Project dataset (Van Essen et al. (2013)).</p>
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