Models for Complex Systems (ModComp)

Course content

The course is an introduction to probability models capable of capturing dependence structures among many observables. The kind of models treated are often called generative models because they directly provide a data generating mechanism. 


Graphical methods play a central role in the course. Graphs provide a natural depiction of dependence but have also a formal mathematical content and are decisive for developing efficient algorithms. 


The theoretical part of the course will be illustrated by a number of concrete applications using data, and a practical application of the theory will be part of the compulsory group project.


The following topics will be covered in the course:

  • Bayesian networks
  • Linear Gaussian networks
  • Models with latent variables
  • Hidden Markov models
  • Gaussian processes 
Learning outcome


  • Graphical representations of dependence and conditional independence 
  • Standard probability propagation algorithms in a network
  • Standard examples of Bayesian networks 
  • Gaussian models 



By the end of the course, the student must 

  • master the graph terminology
  • master the relation between graphs and probability models 
  • be able to decide conditional independence by d-separation
  • be able to implement simulations of variables from a Bayesian network 
  • master computations with linear Gaussian networks based on linear algebra
  • master computations with discrete networks
  • be able to implement ordinary probability propagation algorithms within the framework of Bayesian networks 
  • be able to implement selected learning algorithms and be able to apply them



By the end of the course, the student must

  • be able to decide correctness and relevans of algorithms as well as theoretical computations within the framework of Bayesian networks
  • be able to assess if a Bayesian network correctly represents a specific application
  • be able to assess and discuss the benefits and deficits of an algorithm for a specific Bayesian network, e.g. in terms of run time complexity or generality
  • be able to solve a larger assignment, that includes theoretical as well as practical elements, in collaboration with others

4 hours of lectures and 4 hours of exercises per week for seven weeks.

Will be announced on Absalon

The course is identical to the discontinued course NMAB20002U Modeller for komplekse systemer (ModKomp). Therefore you cannot register for NMAB21009U - Models for Complex Systems (ModComp), if you have already passed NMAB20002U Modeller for komplekse systemer (ModKomp).
If you are registered with examination attempts in NMAB20002U Modeller for komplekse systemer (ModKomp) without having passed the course, you have to use your last examination attempts to pass the exam in NMAB21009U - Models for Complex Systems (ModComp). You have a total of three examination attempts.

Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Continuous assessment
Oral examination, 15 min
The continuous evaluation consists of 3 individual quizzes of one hour each, which will be taken as part of the teaching.

The oral exam will consist of a presentation of a select part of the group report and a subsequent discussion. The oral exam is individual and without preparation.

For the final grade each quiz will count by 1/6 and the oral exam will count by 1/2.

The group report as well as the combined assessment of quizzes can be reused for the reexam the same year and the ordinary exam the year after.
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assessment

See the learning outcomes

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 86
  • Theory exercises
  • 28
  • Project work
  • 60
  • Exam
  • 4
  • English
  • 206