Integrated Nested Laplace Approximations (INLA)

Abstract

Abstract The integrated nested Laplace approximation (INLA) approach provides approximate Bayesian inference in latent Gaussian models (LGMs). INLA relies on a combination of analytical approximations and efficient numerical integration schemes to achieve highly accurate deterministic approximations to posterior quantities of interest. The main benefit of using INLA instead of Markov chain Monte Carlo (MCMC) techniques for LGMs is computational; INLA is fast even for large, complex models. Moreover, being a deterministic algorithm, INLA does not suffer from slow convergence and poor mixing. INLA is implemented in the R package R‐INLA , which represents a user‐friendly and versatile tool for doing Bayesian inference. R‐INLA returns posterior marginals for all model parameters and the corresponding posterior summary information. Model choice criteria as well as predictive diagnostics are directly available. Here, we outline the theory behind INLA, present the R‐INLA package, and describe new developments of combining INLA with MCMC for models that are not possible to fit with R‐INLA .