Approximate Bayesian inference in spatial GLMM with skew normal latent variables

Spatial generalized linear mixed models are common in applied statistics. Most users are satisfied using a Gaussian distribution for the spatial latent variables in this model, but it is unclear whether the Gaussian assumption holds. Wrong Gaussian assumptions cause bias in parameter estimates and affect the accuracy of spatial predictions. Thus, there is a need for more flexible priors for the latent variables, and to perform efficient inference and spatial prediction in the resulting models. In this paper we use skew normal distribution for the spatial latent variables. We propose new approximate Bayesian methods for inference and spatial prediction in this model. A key ingredient in our approximations is using the closed skew normal distribution to approximate the full conditional for latent variables. Our approximate inference and spatial prediction methods are fast and deterministic, using no sampling based strategies.