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Dipankar Bandyopadhyay, Ph.D.
Professor
Department of Biostatistics
Virginia Commonwealth University

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. Our inferential framework is decisively Bayesian, relying on popular Markov chain Monte Carlo tools. Due to the lack of a closed-form density, we introduce approximations, leading to a computationally scalable working model. Motivated by a DTI dataset on cocaine users, we further extend the model to accommodate spatial matrix-variate regression.  Both simulation studies and the real data application demonstrate the improved performance of our model, compared to available univariate (spatial) alternatives.