Fast approximate inference with INLA: the past, the present and the future

Abstract: Latent Gaussian models are an extremely popular, flexible class of models. Bayesian inference for these models is, however, tricky and time consuming. Recently, Rue, Martino and Chopin introduced the Integrated Nested Laplace Approximation (INLA) method for deterministic fast approximate inference. In this paper, we outline the INLA approximation and its related R package. We will discuss the newer components of the r-INLA program as well as some possible extensions.