## Bi8600 Multivariate Methods

Faculty of Science
Autumn 2019
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
RNDr. Jiří Jarkovský, Ph.D. (lecturer)
RNDr. Danka Haruštiaková, Ph.D. (lecturer)
RNDr. Eva Koriťáková, Ph.D. (lecturer)
Mgr. Lucie Brožová (seminar tutor)
RNDr. Simona Littnerová, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jiří Jarkovský, Ph.D.
RECETOX - Faculty of Science
Contact Person: RNDr. Jiří Jarkovský, Ph.D.
Supplier department: RECETOX - Faculty of Science
Timetable
Tue 12:00–14:50 D29/347-RCX2
Prerequisites
Bi5040 Biostatistics or Bi5045 Biostatistics for Computational Biology and Biomedicine. Knowledge on basic unidimensional exploratory statistical techniques, analysis of variance, correlation analysis, simple regression.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is aimed on multivariate data analysis with special emphasis on biological and clinical data. The presented methods extend courses of classical univariate biostatistics: extension of univariate distributions and methods into multivariate space, distance and similarity in multivariate space, cluster analysis, dimensionality reduction throught ordinal methods and discrimination analysis.
Learning outcomes
At the end of the course the student is able to: Prepare a dataset for multivariate analysis correctly; Describe multivariate data; Use multivariate statistical tests; Select appropriate distance or similarity metrics; Compute and visualize association matrices; Apply clustering algorithms and have knowledge of their principles; Apply ordination methods and have knowledge of their principles; Choose appropriate method for multidimensional data analysis based on advantages and limitations of the methods;Interpret results of multivariate analysis.
Syllabus
• Purpose and aims of multivariate data analysis – examples of multivariate data analysis, advantages and disadvantages of multivariate data analysis, data matrices, tabular and graphical visualization of multivariate data.
• Matrix operations, inverse matrix, characteristic polynomial, eigenvalues and eigenvectors, singular value decomposition (SVD)
• Multivariate distributions – random variables, descriptive statistics, confidence interval, outliers
• Multivariate statistical tests – multivariate t-test, multivariate analysis of variance
• Distance and similarity metrics in multidimensional space
• Association matrices – calculation and visualization, descriptive statistics, operations with association matrices (Mantel test, MEANSIM, ANOSIM, association matrix regression)
• Hierarchical cluster analysis – agglomerative methods, divisive methods.
• Non-hierarchical cluster analysis, identification of optimal number of clusters.
• Ordination methods – principles of data reduction, selection and extraction of variables.
• Ordination methods – principal component analysis (PCA)
• Ordination methods – correspondence analysis (CA), multidimensional scaling (MDS)
• Basics of data classification, summary of methods for multivariate data analysis.
Literature
• Legendre, P., Legendre, L. (1998) Numerical ecology. Elsevier, 2nd ed.
• ter Braak, C.J.F. (1996). Unimodal models to relace species to environment. DLO-Agricultural Mathematics Group, Wageningen
• Zar, J.H. (1998) Biostatistical analysis. Prentice Hall, London. 4th ed.
• Flury, B., Riedwyl, H. (1988) Multivariate statistics. A practical approach. Chapman and Hall, London
Teaching methods
Theoretical lectures supplemented by commented examples; students are encouraged to ask questions about discussed topics.
Assessment methods
The final examination is in written form and requires knowledge of multivariate methods principles, prerequisites and application.
Language of instruction
Czech