November 7, 2011

Aalborg Universitet

Daniel Simpson

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 (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 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 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 these lectures I will introduce the required background and theory for understanding INLA, including details on Gaussian Markov random fields and fast computations of those using sparse matrix algorithms. I will end these lectures illustrating INLA on a range of examples in R (see www.r-inla.org).

Organisor: |
Centre for Stochastic Geometry and Advanced Bioimaging (CSGB) and Department of Mathematical Sciences, Aalborg University. |

Location: |
Department of Mathemagical Sciences, Fredrik Bajers Vej 7G, room G5-109. Map |

Fee: | Participation is free but registration is required. Lunch is provided, sponsored by CSGB |

Registration: |
Registration is done by e-mailing secretary Søren Jensen soren@math.aau.dk |

Bring a laptop! |
Participants are encouraged to bring a laptop with R and INLA installed. |

Poster: |
Download a poster announcing the course here. |

Internet access: |
Use Eduroam or AAU-1-day. More information here. |

Notice: |
The short course is followed by the Point process meeting (November 8) and the biannual Two Day Meeting of the Danish Society for Theoretical Statistics (November 8-9). |

9:15 - 12:00 |
Introduction and outline of the course, background. An introduction to Gaussian Markov random fields. Bayesian inference using Integrated Nested Laplace approximations. |

12:00 - 14:00 | Lunch - included for registered participants. Lunch is
served in the Novi canteen. |

14:00 - 16:45 |
Examples and case-studies in R. Spatial models and Log-Gaussian Cox-processes. |