What is INLA?

The integrated nested Laplace approximation (INLA) is a method for approximate Bayesian inference. In the last years it has established itself as an alternative to other methods such as Markov chain Monte Carlo because of its speed and ease of use via the R-INLA package. Although the INLA methodology focuses on models that can be expressed as latent Gaussian Markov random fields (GMRF), this encompasses a large family of models that are used in practice.

This manual describes the INLA program, a new instrument which allows the user to easily perform approximate Bayesian inference using integrated nested Laplace approximation (INLA). We describe the set of models which can be solved by the inla program and provide a series of worked out examples illustrating its usage in details. Appendix A contains a reference manual for the inla program.