Bayesian analysis of spatial generalized linear mixed models with Laplace moving average random fields

Gaussian random field (GRF) models are widely used in spatial statistics to capture spatially correlated error. Gaussian processes can easily be replaced by the less commonly used Laplace moving averages (LMAs) in spatial generalized linear mixed models (SGLMMs). LMAs are shown to offer improved predictive power when the data exhibits localized spikes in the response. Further, SGLMMs with LMAs are shown to maintain analogous parameter inference and similar computing to Gaussian SGLMMs. A novel discrete space LMA model for irregular lattices is proposed, along with conjugate samplers for LMAs with georeferenced and areal support. A Bayesian analysis of SGLMMs with LMAs and GRFs is conducted over multiple data support and response types.