10th Applied Statistics 2013
International Conference
September 22 - 25, 2013
Ribno (Bled), Slovenia
    

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Bayesian computation with INLA


Thiago G. Martins
Department of Mathematical Sciences
Norwegian University of Science and Technology

In this tutorial, 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 spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. The concept of LGM is intended for the modeling stage, but turns out to be extremely usefull 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.

I will introduce the class of latent Gaussian models, describe the "big picture" of the INLA algorithm and introduce the r-INLA package. This is intended to be an applied tutorial, so I will focus on the use of the package on a variety of examples rather than the theory and implementation details behind INLA.

Keywords: Approximate Bayesian inference, INLA, Latent Gaussian models


 Applied Statistics 2013      http://conferences.nib.si/AS2013                                e-mail: info.AS@nib.si