Dipartimento di Statistica, Informatica, Applicazioni "Giuseppe Parenti"

viale Morgagni 59, Firenze - aula 32

# Bayesian computing with INLA: an introduction

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Håvard Rue

Department of Mathematical Sciences, Norwegian University of Science and Technology

In these lectures, 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 the algorithm 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 LGM and INLA; why it works and why its fast. I will end these lectures illustrating INLA on some examples in R. Please visit www.r-inla.org to download the package and for further documentation.

Calendario:

martedì 28 gennaio 2014: 11.30 - 13.00; 14.30 - 16.00

mercoledì 29 gennaio 2014: 10.00 - 11.30