Graphical Models

Course content

  • Markov kernels and conditional distributions
  • Probabilistic conditional independence
  • Conditional independence models
  • Markov properties on directed and undirected graphs
  • Bayesian networks
  • Gaussian graphical models

MSc Programme in Statistics

Learning outcome


Basic knowledge of the topics covered


  • Understand simple properties of conditional distributions and Markov kernels
  • Discuss and understand issues concerning conditional distributions and the interplay between probabilistic and other types of conditional independence
  • Ability to use standard software packages for the analysis of simple graphical models



  • Understand graph based Markov properties and their role for simplification of computation and interpretation
  • Understand properties and limitations of methods for estimating graph structure

Four hours of lectures and three hours of exercises per week for 7 weeks.

Examples of course literature


Previous years have used

S. Lauritzen: Lectures on Graphical Models. Department of Mathematical Sciences, University of Copenhagen, 2018


plus parts of S. Højsgaard, D. Edwards, S. Lauritzen. Graphical Models with R.

Springer-Verlag, New York, 2012.

Basic mathematical statistics and probability based on measure theory.
I.e. Measures and Integrals + Mathematical Statistics or equivalent.

Academic qualifications equivalent to a BSc degree is recommended.

Continuous feedback during the course of the semester

Students receive feedback at the exercise sessions.

7,5 ECTS
Type of assessment
Written assignment, 27 hours
Written take-home assignment
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Theory exercises
  • 18
  • Practical exercises
  • 3
  • Preparation
  • 130
  • Exam
  • 27
  • English
  • 206