Bayesian marginal inference via candidate's formula
Statistics and Computing
A multivariate skew normal distribution
Journal of Multivariate Analysis
Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution
Computational Statistics & Data Analysis
Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap
Computational Statistics & Data Analysis
Approximate inference for disease mapping
Computational Statistics & Data Analysis
Pairwise likelihood inference in spatial generalized linear mixed models
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
On a hybrid data cloning method and its application in generalized linear mixed models
Statistics and Computing
Approximate Bayesian inference for large spatial datasets using predictive process models
Computational Statistics & Data Analysis
Asymptotic normality of posterior distributions for generalized linear mixed models
Journal of Multivariate Analysis
Bayesian computing with INLA: New features
Computational Statistics & Data Analysis
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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 the 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 a skew normal prior distribution for the spatial latent variables. We propose new approximate Bayesian methods for the 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 the latent variables. Our approximate inference and spatial prediction methods are fast and deterministic, using no sampling based strategies. The results indicate that the skew normal prior model can give better predictions than the normal model, while avoiding overfitting.