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Abstract:
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Quantifying spatial associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial dependence is encoded as a latent Gaussian process (GP) in the increasingly common big data settings on which we focus. The scenario worsens in non-Gaussian models because the reduced analytical tractability leads to additional hurdles to computational efficiency. In this article, we introduce a methodology for efficiently computing multivariate Bayesian models of spatially referenced data in which the likelihood or the latent process (or both) are not Gaussian. We exploit the advantages of spatial processes built via directed acyclic graphs, in which case the spatial nodes enter the Bayesian hierarchy and lead to an intuitive algorithm for posterior sampling via routine Markov chain Monte Carlo (MCMC) methods. Our methods compare favorably to state-of-the-art MCMC-free methods, and enable scalable posterior sampling of all unknowns even with data in the millions, as demonstrated on a bivariate spacetime application with misaligned satellite imaging with n > 2.5 * 10^6.
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