E8601 Advanced Statistical Methods

Faculty of Science
Spring 2025
Extent and Intensity
0/3/0. 3 credit(s) (plus extra credits for completion). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
RNDr. Jiří Jarkovský, Ph.D. (lecturer)
RNDr. Michaela Cvanová, Ph.D. (seminar tutor)
Mgr. Lucie Kubínová (seminar tutor)
RNDr. Simona Littnerová, Ph.D. (seminar tutor)
prof. RNDr. Ladislav Dušek, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ladislav Dušek, Ph.D.
RECETOX – Faculty of Science
Contact Person: RNDr. Jiří Jarkovský, Ph.D.
Supplier department: RECETOX – Faculty of Science
Prerequisites
Basic course of biostatistics like Bi5040 Biostatistics - basic course or Bi5045 Biostatistics for computational biology; knowledge of basic univariate statistical methods, analysis of variance, correlation analysis, linear 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 goal of the course is to present area of multivariate statistical methods of biological data in user friendly form aimed on basic principles, limitations and practical interpretation of multivariate analyses. During the course the students will be informed about the methods of description and visualisation of multivariate datasets, basic methods of clustering and ordination analysis and general strategy of multivariate stochastic modelling.
Learning outcomes
After the course the student will be able to:
prepare dataset for multivariate analysis;
describe multivariate data and apply multivariate statistical tests;
select correct association coefficient;
compute and visualise association matrix;
understand and apply clustering algorithms;
understand and apply ordination methods;
understand and apply basic regression models, ANOVA and ROC analysis;
select adequate method of multivariate data analysis based on its advantages, disadvantages and limitations;
interpret results of multivariate data analysis.
Syllabus
  • Aims of multivariate data analysis and modelling – examples of applications, advantages and disadvantages, data matrix, tabular and visual processing of mutivariate data.
  • Matrices - basic mathematical operations, inverse matrix, eigenvalues and eigenvectors.
  • Multivariate statistical distributions - descriptive statistics, confidence interval, outliers.
  • Multivariate statistical tests – multivariate t-test, multivariate ANOVA.
  • Association coefficients in multivariate space.
  • Association matrix – computation and visualisations, descriptive analysis, statistical computations with association matrices (Mantel test, MEANSIM, ANOSIM, regression on association matrices).
  • Hierarchical cluster analysis - hierarchical aglomerative clustering, hierarchical divisive clustering.
  • Nonhierarchical clustering; identification of optimal number of clusters.
  • Ordination analyses – principles of dimensionality reduction, selection and extraction of variables.
  • Ordination analyses – principal component analysis (PCA).
  • Ordination analyses – correspondence analysis (CA), multidimensional scaling (MDS).
  • Ordination analyses - discrimination analysis.
  • Basic principles of stochastic modelling - ANOVA, linear regression, ROC analysis, logistic regression, strategy of regression modelling.
  • Summary of multivariate methods application in data analysis.
Literature
  • LEGENDRE, Pierre and Louis LEGENDRE. Numerical ecology. 3rd engl. ed. Amsterdam: Elsevier, 2012, xvi, 990. ISBN 9780444538680. info
  • BORCARD, Daniel, François GILLET and Pierre LEGENDRE. Numerical ecology with R. New York: Springer, 2011, xi, 306. ISBN 9781441979759. info
  • ZAR, Jerrold H. Biostatistical analysis. 5th ed. Upper Saddle River, N.J.: Prentice Hall, 2010, xiii, 944. ISBN 9780131008465. info
Teaching methods
Theoretical lectures supplemented by commented examples and computer practise. Discussion of students is encouraged.
Assessment methods
Written exam aimed on principles of multivariate methods, prerequisites of computations, their application and interpretation.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2023, Spring 2024.
  • Enrolment Statistics (Spring 2025, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2025/E8601