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Title: Spatial meshing and manifold preconditioning for Bayesian analysis of non-Gaussian data Authors:  Michele Peruzzi - Duke University (United States) [presenting]
David Dunson - Duke University (United States)
Abstract: 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 large-scale 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. We introduce methodologies for efficiently computing multivariate Bayesian models of spatially referenced non-Gaussian data. First, we outline spatial meshing as a tool for building scalable processes using patterned directed acyclic graphs. Then, we introduce a novel Langevin method which achieves superior sampling performance with non-Gaussian multivariate data that are common in studying species' communities. We proceed with outlining strategies for improving Markov-chain Monte Carlo performance in the settings on which we focus. We conclude with extensions and applications showcasing the flexibility of the proposed methodologies and the publicly-available software package.