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Abstract:
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We study a setting where the spatial surface of interest has unknown dependency on another non-overlapping spatial surface, over which we have measured data. The two surfaces can have drastically different underlying spatial structure, so that we may model one as continuous while another as defined on an undirected graph. In this setting, we propose a flexible Bayesian hierarchical regression model that linearly maps the measured predictors from the non-overlapping surface to the surface for response. A novel, spatially informed shrinkage prior is placed on the vectorized coefficient matrix that maps one surface to another. Simulation results show our method improves upon naïve spatial analyses that do not include predictors from a non-overlapping surface. Finally, we apply the method to optical coherence tomography (OCT) scans of the glaucoma patients’ macula region and optic nerve head retinal nerve fiber layer (RNFL), two non-overlapping images of the retina. Our results demonstrate clinical utility of the method, as inference from the macula OCT is improved when incorporating RNFL measures.
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