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Abstract:
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Geostatistical modeling has been extensively applied to model continuous point-referenced neuroimaging data, because of its potential in producing efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging technique, produces voxel-level positive definite (p.d) matrices as responses, which available geostatistical modeling tools are unable to handle efficiently. In this talk, we propose the spatial Wishart process, a spatial stochastic process, where each p.d matrix-variate responses marginally follows a Wishart distribution, with the spatial dependence induced by latent Gaussian processes. This process is valid on an uncountable collection of spatial locations, and is almost surely continuous. Motivated by a DTI dataset of cocaine users, we further extend the model to accommodate spatial matrix-variate regression. Due to the lack of a closed-form density, we introduce approximations leading to a computationally scalable working model. Both simulation studies and the real data application demonstrate the improved performance of our model, compared to available univariate spatial alternatives.
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