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
Education

MSc Programme in Statistics

Learning outcome

Knowledge:

Basic knowledge of the topics covered

Skills:

  • 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

 

Competences:

  • 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.

Oral
Continuous feedback during the course of the semester

Students receive feedback at the exercise sessions.

ECTS
7,5 ECTS
Type of assessment
Written assignment, 27 hours
Written take-home assignment
Aid
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