MA850 Statistical Inference for Multivariate Data

Faculty of Science
Autumn 2019
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 MS1,01016
Prerequisites
M6120 Linear statistical models II, M7986 Statistical inference I a M8986 Statistical inference II.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The main goal of the course is to become familiar with some basic principles of testing statistical hypotheses about vectors and matrices of parameters base on Wald principle, likelihood and score principle, their implementation in R, geometry, numerical optimisation, and statistical graphics for continuous and discrete data. At the end of this course, the student will be able (1) to understand and explain basic principles of parametric statistical inference for continuous and discrete data for multivariate parameters (vectors and matrices), (2) to implement these techniques into R language, and (3) to be able to apply them to real data.
Learning outcomes
Student will be able:
- to understand principles of likelihood and statistical inference of vectors and matrices of parameters for for multivariate continuous and discrete data;
- to select suitable probabilistic and statistical model in statistical inference of vectors and matrices of parameters for for multivariate continuous and discrete data;
- to build up and explain suitable statistical test of vectors and matrices of parameters for for multivariate continuous and discrete data;
- to apply statistical inference on real multivariate continuous and discrete data;
- to implement methods of statistical inference for multivariate continuous and discrete data in R.
Syllabus
  • Testing of hypotheses about mean vector, vector of variances, vector of correlation coefficients and vector of probabilities (multi-sample problems, Wald, likelihood and score principle), generalized tests with constrains.
  • Testing of hypotheses about mean vectors, covariance matrices for one-, two-, and multi-sample problems, profile analysis, MANOVA, generalized tests with constrains.
  • Testing of hypotheses in multiple linear regression model about vector of regression coefficients, multiple correlation coefficient and partial correlation coefficient (Wald principle and likelihood principle), generalisation for multivariate multiple linear regression model, generalized tests with constrains.
  • Principal component analysis, asymptotic properties of principal components (eigenvalues and eigenvectors), normalized (standardized) principal components, common principal components, factor analysis, discriminant analysis, canonical correlation analysis and correspondence analysis.
  • Implementation to R and applications on real multivariate data from biology, medicine and other fields.
Literature
    recommended literature
  • KATINA, Stanislav, Miroslav KRÁLÍK and Adéla HUPKOVÁ. Aplikovaná štatistická inferencia I. Biologická antropológia očami matematickej štatistiky (Applied statistical inference I). 1st ed. Brno: Masarykova univerzita, 2015, 320 pp. 1. ISBN 978-80-210-7752-2. info
  • Applied multivariate statistical analysis. Edited by Richard Arnold Johnson - Dean W. Wichern. 6th ed. Upper Saddle River, N.J.: Pearson Prentice Hall, 2007, xviii, 773. ISBN 9780131877153. info
  • MARIDA, K. V., J. T. KENT and J. M. BIBBY. Multivariate analysis. London: Academic press, 1979, xv, 518. ISBN 0124712525. info
Teaching methods
Lectures: 2 hours per week.
Assessment methods
Homework, oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2019, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2019/MA850