An overview of the Integrated Nested Laplace Approximation (INLA) methodology
The Integrated Nested Laplace Approximation (INLA) is a method for performing fast and accurate approximate Bayesian inference. Over recent years, INLA has become a compelling alternative to traditional approaches like Markov chain Monte Carlo (MCMC), primarily due to its remarkable speed and simplicity when used through the R-INLA package.
While INLA is tailored for models that can be formulated as Latent Gaussian Markov Random Fields (GMRFs), this class encompasses a wide array of commonly used models in practice. The method strategically exploits the sparsity and structure of these models to perform efficient inference.