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Lecturer(s)
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Hron Karel, prof. RNDr. Ph.D.
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Fačevicová Kamila, Mgr. Ph.D.
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Course content
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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. Dimension reduction - SVD, PCA, biplot and its interpretation 4. Cluster analysis - hierarchical clustering (dendrogram), k-nearest neighbor method, fuzzy clustering 5. Classification methods - LDA, QDA, Fisher discriminant analysis. 6. Basics of robust statistics - regression analysis 7. Basics of robust statistics - estimation of location and scale, properties (MCD) 8. PARAFAC - generalization of PCA, construction of the model, estimation of parameters, graphical output and its interpretation 9. PLS regression and its application in classification, comparison with the classical approach (LDA, QDA) 10. Methods of parameter estimation in PLS regression. 11. Comparing several groups - MANOVA 12. Complex analysis of a data set
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
- Attendace
- 52 hours per semester
- Preparation for the Course Credit
- 20 hours per semester
- Preparation for the Exam
- 30 hours per semester
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Learning outcomes
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Understand basic methods of multivariate statistical analysis including their implementation in statistical software R. Active participation.
Application Apply probability theory to methods of multivariate statistical analysis.
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Prerequisites
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Basic knowledge of probability theory and mathematical statistics.
KMA/PST
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Assessment methods and criteria
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Oral exam
Credit: comprehensive statistical processing of a data set, presentation of results. Exam: oral.
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Recommended literature
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B. Everitt, T. Hothorn. (2011). An introduction to applied multivariate analysis with R. Springer, Heidelberg.
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Budíková, M. (2014). Využití vícerozměrné analýzy rozptylu v psychometrii. Kvaternion 3 (1), 3-15.
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G. James, D. Witten, T. Hastie, R. Tibshirani. (2014). An introduction to statistical learning, corr. 4th printing. Springer, New York.
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Giordani, P., Kiers, H.A.L., Del Ferraro, M.A. (2014). Three-way component analysis using the R package ThreeWay. Journal of Statistical Software 57 (7), 1-23.
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K. Varmuza, P. Filzmoser. (2008). Introduction to multivariate statistical analysis in chemometrics. CRC Press, Boca Raton.
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R. Maronna, R. D., Martin, V.J. Yohai. (2006). Robust statistics: Theory and methods. John Wiley, New York.
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R. Wehrens. (2011). Chemometrics with R. Springer, Heidelberg.
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