PhD course on Gaussian Markov random fields

This PhD level course was given at Chalmers University of Technology in 2015. It consisted of 10 lectures and 2 projects and was primarily based on the book "Gaussian Markov Random Fields, Theory and Applications" by Rue and Held.

Lecture 1 - Introduction to the course.

slides

Lecture 2 - Definition and properties of GMRFs.

slides

Lecture 3 - Computational methods for GMRFs.

slides

Lecture 4 - Numerical methods for sparse matrices.

slides

Lecture 5 - Intrinsic GMRFs

slides

Lecture 6 - MCMC for hierarchical models.

slides

Lecture 7 - MCMC and INLA.

slides

Lecture 8 - Introduction to the SPDE approach.

slides

Lecture 9 - The SPDE approach, part 2

slides

Lecture 10 - Applications, extensions and software.

slides

Project 1 - GMRFs and image restoration.

project description

Data: rosetta_large | rosetta_small | titan

slides

Project 2 - SPDE models and INLA.

project description

Data: USdata

slides

Many of the slides were borrowed from earlier courses on GMRFs and INLA given by Dan Simpson and others. The first project was inspired by a project on GMRFs developed by Finn Lindgren while giving the course on statistical image analysis at Lund University.