Course content

The course will give a theoretical and methodological introduction and discussion of computational intensive statistical methods, but assumes also good computational skills. Topics to be discussed are a selection of the following; theory and methods for Markov chain Monte Carlo, sequential Monte Carlo methods, Hidden Markov chains, Gaussian Markov random fields, mixtures, non-parametric methods and regression, splines, graphical models, latent Gaussian models and their approximate Bayesian inference. Relative weighting of the various topics will vary according to need.

Learning outcome

1. Knowledge. The course gives a theoretical and methodological introduction and discussion of computational intensive statistical methods, but assumes also good computational skills. Topics to be discussed are a selection of the following; theory and methods for Markov chain Monte Carlo, sequential Monte Carlo methods, Hidden Markov chains, Gaussian Markov random fields, mixtures, non-parametric methods and regression, splines, graphical models, latent Gaussian models and their approximate Bayesian inference. 2. Skills. The students should be able to use the basic computational intensive techniques in the modern theoretical statistics. In particular, Markov chain Monte Carlo, sequential Monte Carlo methods, Hidden Markov chains, Gaussian Markov random fields, mixtures, non-parametric methods and regression, splines, graphical models, latent Gaussian models and their approximate Bayesian inference. 3. Competence. The students should be able to participate in scientific discussions and conduct researches in statistics on high international level. They should be able to participate in applied projects involving statistical methods and apply their knowledge in problems in theoretical statistics.

Learning methods and activities

This subject is normally taught every second year, next time spring 2026. A condition is that sufficiently many students are registered. Lectures, alternatively guided self-study if there are only few students. The content and form of the obligatory activities will be given at semester start.

Compulsory assignments

• Obligatory activities

Recommended previous knowledge

TMA4315 Generalized Linear Models

Required previous knowledge

TMA4300 Computer Intensive Statistical Methods, TMA4295 Statistical Inference, TMA4267 Linear statistical models, or equivalent. Good understanding and experience with R, or another high-level programming language.

Course materials

Will be announced at the start of the course.