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Abstract:
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Primarily in the context of multivariate or spatiotemporal disease risk mapping and inference, multidimensional Gaussian Markov random fields (MGMRFs), formulated via latent conditionals and coregionalization, have received recent attentions on their capacities for (1) characterizing multidimensional spatial dependencies, (2) modeling covariance and cross-covariance functions, and (3) facilitating borrowing-information and intelligent smoothing. I review key progress made to date and highlight nuanced MGMRF parameterizations that aspire to enrich and broaden the scope of disease mapping efforts. I give emphasis on MGMRF parameterizations for latent spatial components representation and present MGMRF examples for shared component analysis, principal spatial components analysis, and parameterization for dimension reduction. I illustrate applications to disease mapping and small area estimation. I conclude with a summary discussion of potential work for MGMRF development in the context of spatial and image data analytics.
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