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PřF:MA850 Statistical Inference for Mult - Course Information

## MA850 Statistical Inference for Multivariate Data

**Faculty of Science**

autumn 2021

**Extent and Intensity**- 2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).

Taught in person. **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**- Wed 8:00–9:50 MP2,01014a
**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**- 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

*recommended literature*- KATINA, Stanislav, Miroslav KRÁLÍK and Adéla HUPKOVÁ.
**Teaching methods**- Lectures: 2 hours per week. On-line using MS Teams or full-time according to the according to the development of the epidemiological situation and the applicable restrictions.
**Assessment methods**- Homework, oral exam. The conditions may be specified according to the development of the epidemiological situation and the applicable restrictions.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course is taught annually. **Teacher's information**- The lectures 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 lectures will take place online at MS Teams at the time of the normal lectures according to the schedule. Due to the possible low signal quality, I recommend students not to use the camera. Questions during the lecture will not be possible to ask by voice, but by chat.

The recording from the lecture will be uploaded in the IS sequentially and not in advance, so the recording will be uploaded only after the given lecture and before the next lecture. The recordnig does not have to contain a complete lecture, it is up to a teacher what to share from the record and share it with the students. What is a lecture recording? It can be a PDF of text written by the lecturer on the screen with an electronic pen during the lecture, and this can be supplemented by the voice (or voice and video) of the lecturer. Slides in PDF with TeX-ed text will always be available in the IS and will be shared only after the given lecture and before the next lecture.

Consultations about the lectures will take place through a discussion forum, where the lecturer / instructor moderates this discussion and new discussion forums established by students will not be taken into account. Discussion forums will be based on individual lectures and practicals (if the course has practicals) and about homework. Discussions by e-mail will not take place.

- Enrolment Statistics (recent)

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