Date: 5-6. November 2014 (ends about 12 a.m. November 6th)If you are interested to participate, please contact Bettina Kulle Andreassen
Instructor: Andrea Riebler, Department of Mathematical Sciences, Norwegian University of Science and Technology
In this course, I will discuss approximate Bayesian inference for a class of models named latent Gaussian models (LGM). LGM's are perhaps the most commonly used class of models in statistical applications. It includes, among others, most of (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatio-temporal models, log-Gaussian Cox processes and geostatistical and geoadditive models.
The concept of LGM is intended for the modelling stage, but turns out to be extremely useful when doing inference as we can treat models listed above in a unified way and using the *same* algorithm and software tool. Our approach to (approximate) Bayesian inference, is to use integrated nested Laplace approximations (INLA). Using this tool, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. 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.
In this course, I will introduce the class of latent Gaussian models, describe the "big picture" of the INLA algorithm and introduce the R-INLA package. I will focus on applied aspect and the use of the package illustrated on several examples rather than the theory and implementation details behind INLA. This is intended to be an applied tutorial, where lectures are combined with computer sessions.
Required background: Basic knowledge in Bayesian modelling and R.