Graphical Models

Weight: 4 modules

Aims:

• To provide understanding of the theory of graphical models and their applications
• To provide knowledge of basic graphical model software

Mathematics and statistics from the undergraduate courses.  It is advantageous to follow courses on the Multivariate Gaussian Distribution and on standard Measure Theory simultaneously.

Contents:

A preliminary list of contents is the following:

Conditional independence, Markov properties for undirected graphs and directed acyclic graphs, graphical models for contingency tables,  log-linear hierarchical models, Bayesian networks and probabilistic expert systems, graphical models for complex data structures. Software such as HUGIN, CoCo, and BUGS.

The course might develop as it goes along.

Textbook:

S. L. Lauritzen, Graphical Models. Oxford University Press, Oxford, 1996.

Supplementary material:

There will be used much supplementary material from manuals to the software programs and from

S. L. Lauritzen, Lectures on Contingency Tables, 3rd edition. Aalborg University, 1989.

The last item can be obtained from Lisbeth Grubbe Nielsen, FrB7, E4-104.

There will also be used selected articles and ad-hoc notes.

Assessment:

Assessment is based on a graded oral exam combined with one or more miniprojects during the course (pass/not pass), each of which resulting in a written report (to be delivered by groups of 2 - 3 students).