ABSTRACT
Bayesian hierarchical models are often used to model spatial and spatio-temporal data. These models allow complete flexibility in how estimates borrow strength across space and time, and improve estimation and prediction of the underlying model features. Integrated nested Laplace approximation (INLA) uses a combination of analytical approximations and numerical algorithms for sparse matrices to approximate the posterior distributions with closed-form expressions. This allows faster inference and avoids problems of sample convergence and mixing which permit to fit large datasets and explore alternative models. INLA allows to perform approximate Bayesian inference in latent Gaussian models such as generalized linear mixed models and spatial and spatio-temporal models. The approximations for the posterior marginals for the conditioned on selected values can be obtained using a Gaussian, a Laplace, or a simplified Laplace approximation. The dimension of the hyperparameter vector should be small because approximations are computed using numerical integration over the hyperparameter space.
