Multivariate Data Analysis 7.5 credits

About the course

The course provides the basic theory and methods for multivariate data analysis and lays a solid foundation for learning more advanced methods and algorithms in the next step. It starts from multivariate Gaussian distribution (MGD) and its generalization, the Gaussian mixture model. The maximum likelihood estimation (MLE) and the EM algorithm are discussed. Based on MGD, statistical inference approaches (Hotelling's T square test, multivariate analysis of variance, MANOVA), classification methods (Linear discriminant analysis and logistic regression), and clustering analysis methods are covered. Furthermore, based on the projection ideas, different eigen-decomposition based methods for dimensionality reduction, such as principal component analysis (PCA), factor analysis (FA), canonical correlation analysis (CCA), and partial least squares (PLS) are introduced. Models for regression analysis with colinear explanatory variables such as principal component regression (PCR) and PLS regression are also included.

Module 1 (5 hp): Theory and applications
The module covers multivariate distributions with special emphasis on the multivariate normal distribution and its properties. The EM algorithm for finding maximum likelihood estimation of GMM is introduced. Further, methods for inference concerning mean vectors, and variance and correlation matrices are treated, along with methods for projections, classification, and clustering analysis.

Module 2 (2,5 hp): Computer labs
Multivariate data analysis with suitable statistical software. The module includes written and oral presentation of results.

Show syllabus

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Autumn 2025
- Multivariate Data Analysis
  
  Second admissions round for EU/EEA citizens
  
  Autumn 2025 / Umeå / English / On site
  
  Show more Show less
  
  Starts
  1 September 2025
  
  Ends
  2 November 2025
  
  Number of credits
  7.5 credits
  
  Type of studies
  On site
  
  Study pace
  50%
  
  Teaching hours
  Daytime
  
  Study location
  Umeå
  
  Language
  English
  
  Application code
  UMU-58207
  
  Eligibility The course requires 90 ECTS including courses in Mathematical Statistics, minimum 12 ECTS, or courses in Statistics, minimum 75 ECTS and in both cases a course in Basic Calculus, 7,5 ECTC and a course in Linear algebra, 7,5 ECTS, or equivalent. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies.
  
  Selection
  Guaranteed place
  
  Application
  Application deadline was 15 April 2025. The application period is closed. Please note: This second application round is intended only for EU/EEA/Swiss citizens.
  
  Application and tuition fees
  As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.
  
  Application fee: SEK 900
  
  Tuition fee, first instalment: SEK 19,038
  
  Total fee: SEK 19,038
  
  Details about tuition, fees and funding

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