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An introduction to Bayesian computing with INLA (1 day)

Dates: July 8th

Leaders: Håvard Rue & Elias Krainski (Norwegian University of Science and Technology, Norway)

Håvard Rue is professor in statistics at the Department of Mathematical Sciences, Norwegian University of Science and Technology. His research interest includes Bayesian computing and spatial statistics, which is summarised through R-INLA package, see He has been an associate editor for JRSS series-B, Scandinavian Journal of Statistics, Statistic Surveys, Annals of Statistics and Environmetrics. His main research interest has been Gaussian Markov random fields (GMRF) models, and with Leonhard Held he has written a monograph on the subject published by Chapman & Hall. GMRFs is also a main ingredient doing (fast and accurate) approximate Bayesian analysis for latent Gaussian models using integrated nested Laplace approximations (INLA), which is published as a discussion paper for JRSS series B 2009 co-authored with S.Martino and N.Chopin. GMRFs also appears within geostatistics using stochastic partial differential equations as the bridge, which provides an explicit link between certain Gaussian fields and GMRFs in triangulated lattices (published as a discussion paper for JRSS series B in 2011, with F.Lindgren and J.Lindstrøm).

Elias T. Krainski is assistant professor (licensed to get PhD) at Federal University of Parana, Brasil and PhD candidate at the Department of Mathematical Sciences, Norwegian University of Science and Technology. His research interest includes spatial and spatio-temporal models and on developing models that allows fast computations.

Description: In this short 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 (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 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 thesamealgorithm 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. 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 short course I will introduce the background for understanding LGMs and INLA; why it works and why its fast. I will end these lectures illustrating INLA on some spatial examples using the R-INLA package, where we use stochastic partial differential equation (SPDE) approach to formulate the spatial component in the Baysian model.

Please visit to download the package and for further documentation.


  • 09.00-10.30 Overview R-INLA (part I)
  • 10.30-11.00 Break
  • 11.00-12.30 Overview R-INLA (part II)
  • 12.30-14.30 Lunch
  • 14.30-15.30 Spatial models in R-INLA: an overview
  • 15.30-16.00 Break
  • 16.00-17.00 Spatial models in R-INLA: a case study

Workshop material: The course material can be downloaded from the here.