Inference for spatial generalized linear mixed models (SGLMMs) forhigh-dimensional non-Gaussian spatial data is computationally intensive. Thecomputational challenge is due to the high-dimensional random effects andbecause Markov chain Monte Carlo (MCMC) algorithms for these models tend to beslow mixing. Moreover, spatial confounding inflates the variance of fixedeffect (regression coefficient) estimates. Our approach addresses both thecomputational and confounding issues by replacing the high-dimensional spatialrandom effects with a reduced-dimensional representation based on randomprojections. Standard MCMC algorithms mix well and the reduced-dimensionalsetting speeds up computations per iteration. We show, via simulated examples,that Bayesian inference for this reduced-dimensional approach works well bothin terms of inference as well as prediction; our methods also compare favorablyto existing "reduced-rank" approaches. We also apply our methods to two realworld data examples, one on bird count data and the other classifying rocktypes.
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