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Abstract:
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A large number of scientific studies and engineering problems involve high-dimensional spatiotemporal data with complicated relationships. In this talk, we focus on a type of space-time interaction named \emph{temporal evolution of spatial dependence (TESD)}, which is a zero time-lag spatiotemporal covariance. For this purpose, we propose a novel Bayesian nonparametric method based on non-stationary spatiotemporal Gaussian process (STGP). The classic STGP has a covariance kernel separable in space and time, failed to characterize TESD. We generalize STGP (gSTGP) to introduce the time-dependence to the spatial kernel by varying its eigenvalues over time in the Mercer's representation. The resulting non-separable non-stationary covariance model bares a quasi Kronecker sum structure. Finally, a hierarchical Bayesian model for the joint covariance is proposed to allow for full flexibility in learning TESD. A simulation study and a longitudinal neuroimaging analysis on Alzheimer's patients demonstrate that the proposed methodology is (statistically) effective and (computationally) efficient in characterizing TESD.
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