Tutorial 3: Bayesian Computing with INLA -- Håvard Rue

In this lecture, I will discuss approximate Bayesian inference for the class of latent Gaussian models (LGMs). LGMs are perhaps the most commonly used class of models in statistical applications. It includes, among others, most of (generalised) linear models, (generalised) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. The concept of LGMs is extremely useful when doing inference as we can treat models listed above in a unified way and using the same algorithms and software tool. Our approach to (approximate) Bayesian inference, is to use integrated nested Laplace approximations (INLA). Using this new tool, we can directly compute very accurate approximations to the posterior marginals. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged. I will discuss the background for understanding LGM and INLA, end by illustrating INLA on some examples in R. Please visit www.r-inla.org to download the package and for further information.