NMAK22007U Models for Complex Systems (ModComp)

Volume 2022/2023

MSc Programme in Statistics
MSc Programme in Mathematics-Economics


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

Will be announced on Absalon

The course is targeted towards MSc students in statistics, computer science, or similar. Participants are expected to have corresponding mathematical and computational qualifications, for example, by having passed a BSc level course in linear algebra, and either the courses MatStat and StatMet (formerly Mathematical Statistics) or the courses Machine Learning A and Machine Learning B.
4 hours of lectures and 4 hours of exercises per week for seven weeks.
The course is identical to the discontinued courses NMAB20002U Modeller for komplekse systemer (ModKomp) and NMAB21009U Models for Complex Systems (ModComp). Therefore you cannot register for NMAK22007U Models for Complex Systems (ModComp), if you have already passed either one of the two discontinued courses.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 86
  • Theory exercises
  • 28
  • Project work
  • 60
  • Exam
  • 4
  • Total
  • 206
Continuous feedback during the course
7,5 ECTS
Type of assessment
Continuous assessment
Oral examination, 15 min
Type of assessment details
The students must write and hand in a report in groups of 4-6 individuals. The report will form the basis for the oral exam, and the report must be handed in to participate in the oral exam

In addition, 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 student's two best quiz scores will count by 1/4 and the oral exam will count by 1/2.
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship

Written report, oral exam without preparation (as in the ordinary exam) and a 3-hour quiz. 


The student has the possibility to reuse the group report from the ordinary exam as the basis for the oral reexam, but they are also allowed to hand in a new report.
If the student did not hand in a group report, they must hand in a new report.
If necessary, the report can be made on an individual basis.
The report must be handed in no later than 3 weeks before the first day in the re- exam week.


The student has the possibility to reuse the combined assesment of the quizzes taken during the teaching, but they also have the opportunity to retake all quizzes by taking one combined, 3-hour quiz based on new questions. It is only possible to retake all 3 quizzes, in which case the final grade will be based on the assessment of the new quizzes.

Criteria for exam assesment

See the learning outcomes