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Abstract:
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Non-Gaussian spatial data are prevalent across many fields (e.g., animal counts in ecology, count data on disease incidence, pollutant concentrations near highways, and the incidence of cloud cover in satellite imagery). Spatial generalized linear mixed models are a highly flexible class of spatial models for non-Gaussian spatial data, but these can be computationally prohibitive for large datasets. To address this challenge, past studies approximate the spatial random field using basis functions; thereby exploiting the low-rank structures and bypassing large matrix operations. Popular basis representation methods employ nested radial basis functions with fixed knot locations and bandwidths, but these must be fixed a priori and this specification affects model performance. We propose a data-driven, adaptive algorithm that results in increased flexibility and fast model-fitting: (1) the knot locations are selected based on a space-covering design; (2) we partition the spatial domain into disjoint subregions such that the smoothing parameter varies across partitions; and (3) in our Bayesian model, the smoothing parameters are allowed to vary. Our approach extends to a wide array of s
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