  Nonstationary and non-Gaussian spatial data are common in various fields,
including ecology (e.g., counts of animal species), epidemiology (e.g., disease
incidence counts in susceptible regions), and environmental science (e.g.,
remotely-sensed satellite imagery). Due to modern data collection methods, the
size of these datasets have grown considerably. Spatial generalized linear
mixed models (SGLMMs) are a flexible class of models used to model
nonstationary and non-Gaussian datasets. Despite their utility, SGLMMs can be
computationally prohibitive for even moderately large datasets (e.g., 5,000 to
100,000 observed locations). To circumvent this issue, past studies have
embedded nested radial basis functions into the SGLMM. However, two crucial
specifications (knot placement and bandwidth parameters), which directly affect
model performance, are typically fixed prior to model-fitting. We propose a
novel approach to model large nonstationary and non-Gaussian spatial datasets
using adaptive radial basis functions. Our approach: (1) partitions the spatial
domain into subregions; (2) employs reversible-jump Markov chain Monte Carlo
(RJMCMC) to infer the number and location of the knots within each partition;
and (3) models the latent spatial surface using partition-varying and adaptive
basis functions. Through an extensive simulation study, we show that our
approach provides more accurate predictions than competing methods while
preserving computational efficiency. We demonstrate our approach on two
environmental datasets - incidences of plant species and counts of bird species
in the United States.
