The R-INLA software package implements Bayesian analysis of a class of models named latent Gaussian models. This sounds pretty boring, but latent Gaussian models are nothing else than an abstract formulation of a huge class which covers most statistical models that are in regular use. In my view, it is the most important class of statistical models. The R-INLA package is based on some key methodological developments, like integrated nested Laplace approximations for the approximate Bayesian inference, and stochastic partial differential equations to represent (spatial) Gaussian fields, a model formulation based on Gaussian Markov random fields and computations based on numerical methods for sparse matrices. All this gets somewhat technical, but the end result from the users perspective is simply easy access to advanced hierarchical models with fast computing time that scale well with the dimension of the model.

In this talk, I will give an introduction to R-INLA and the basic ideas, and discuss some recent developments and current directions of research within the 'R-INLA project'.