Course: Applications of Multivariate Statistics Methods

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Course title Applications of Multivariate Statistics Methods
Course code KMA/AMMS
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Hron Karel, doc. RNDr. Ph.D.
Course content
1. Basic properties of multivariate random sample, the role of software in multivariate statistical analysis 2. Explorative statistical analysis of univariate and multivariate data sets (methods of data visualization, descriptive methods, data quality - outliers and missing values) 3. Cluster analysis - hierarchical clustering (dendrogram), k-nearest neighbor method, fuzzy clustering 4. Cluster analysis using self organizing maps (SOM) 5. Basics of robust statistics - regression analysis 6. Basics of robust statistics - estimation of location and scale, properties (MCD) 7. Dimension reduction - SVD, PCA, biplot and its interpretation, robust alternatives 8. PARAFAC - generalization of PCA, construction of the model 9. PARAFAC - estimation of parameters, graphical output and its interpretation 10. PLS regression and its application in classification, comparison with the classical approach (LDA,QDA) 11. Comparing several groups - MANOVA 12. Complex analysis of a data set

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
  • Attendace - 39 hours per semester
  • Preparation for the Exam - 30 hours per semester
  • Preparation for the Course Credit - 20 hours per semester
Learning outcomes
Understand advanced methods of multivariate statistical analysis inclusive their implementation in statistical software R.
Application Apply probability theory to methods of multivariate statistical analysis.
Prerequisites
Basic knowledge of probability theory and mathematical statistics.

Assessment methods and criteria
Oral exam, Written exam

Credit: the student has to pass a written test (one whole example out of two must be correct), credit project (multivariate statistical analysis of a data set in statistical SW). Exam: pass written test (at least one whole example out of two correct), the student has to understand the subject and be able to prove the principal results.
Recommended literature
  • Anderson, T. W. (2003). An introduction to multivariate statistical analysis. Wiley-Interscience, Hoboken.
  • Härdle, W., & Simar, L. (2003). Applied multivariate statistical analysis. Springer-Verlag, Berlin.
  • Hebák, P., Hustopecký, J., & Malá, I. (2005). Vícerozměrné statistické metody. Praha: Informatorium.
  • Hebák, P., Hustopecký, J., Jarošová, E., & Pecáková, I. (2007). Vícerozměrné statistické metody. Praha: Informatorium.
  • Hebák, P., Hustopecký, J., Pecáková, I., Plašil, M., Řezanková, H., Vlach, P., & Svobodová, A. (2007). Vícerozměrné statistické metody. Praha: Informatorium.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applications of Mathematics in Economy (2015) Mathematics courses 2 Winter
Faculty of Science Applied Mathematics (2014) Mathematics courses 2 Winter