ST811: Multivariate Statistical Analysis

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N370003102
Assessment: Second examiner: None
Grading: Pass/Fail
Offered in: Odense
Offered in: Spring
Level: Master's level course approved as PhD course

STADS ID (UVA): N370003101
ECTS value: 5

Date of Approval: 26-10-2018

Duration: 1 semester

Version: Archive


25002401 (former UVA) is identical with this course description. 
The course is co-read with: ST514 Multivariate statistical analysis
The course cannot be chosen by students who have passed ST514

Entry requirements

A Bachelor’s degree in Science or an equivalent study programme.

Academic preconditions

Students taking the course are expected to:
  • have skills in
    statistics corresponding to ST520 Applied statistics or ST521
    Mathematical statistics, and calculus corresponding to one of the
    calculus courses on the first year on the study programmes at the
    Faculty of Science, SDU
  • be able to use the statistical software R

Course introduction

The aim of the course is to enable the student to work systematically
with data sets with several variables, which is important in regard to
performing statistical analyses in a broad range of research areas, such
as biology and epidemiology

The course builds on the knowledge
acquired in the courses such as ST520 Applied statistics or ST521
Mathematical statistics, and the calculus course in the respective study
programme, and gives an academic basis for studying topics such as
biometry, that are part of the degree, as well as master projects where
multivariate methods are employed.

In relation to the competence profile of the degree it is the explicit focus of the course to:

  • Give the competence to evaluate and choose between different methods for the analysis of multivariate data sets 
  • Give skills to perform analyses of multivariate data sets using the statistical software R
  • Give knowledge and understanding of  the fundamental ideas and methods for analyzing measurements on several variables

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

  • reproduce
    key theoretical results concerning elementary operations on random
    variables and random vectors, and to apply these to simple theoretical
  • work with the concepts and models, both in scalar and matrix/vector representation  
  • understand and identify problems that can be solved using multivariate techniques  
  • perform a practical data analysis with the techniques from the course  
  • perform programming relevant to the content of the course in the statistical package used in the course  
  • identify and interpret relevant information in the output of the statistical package used in the course  
  • summarize the results of an analysis in a statistical report


The following main topics are contained in the course:
  • random vectors
  • the multivariate normal distribution
  • inference about a mean vector
  • comparison of several mean vectors
  • principal component analysis
  • discriminant analysis and classification


See Blackboard for syllabus lists and additional literature references.

Examination regulations

Exam element a)




Oral exam




Second examiner: None




Student Identification Card


Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value


Additional information

Oral exam based on written project reports, handed in during the course

The examination form for re-examination may be different from the exam form at the regular exam.

Indicative number of lessons

48 hours per semester

Teaching Method

In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours aor the study phase hours.

Educational activities 

  • Work on problems not covered in the training phase
  • Discussion of the concepts and terms of the topic

Teacher responsible

Name E-mail Department
Hans Christian Petersen


Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration


Offered in


Recommended course of study

Profile Education Semester Offer period