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PřF:M7986 Statistical inferences I - Course Information

## M7986 Statistical inferences I

**Faculty of Science**

Autumn 2020

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

Taught online. **Teacher(s)**- doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)

Mgr. Veronika Horská (seminar tutor) **Guaranteed by**- doc. PaedDr. RNDr. Stanislav Katina, Ph.D.

Department of Mathematics and Statistics - Departments - Faculty of Science

Contact Person: doc. PaedDr. RNDr. Stanislav Katina, Ph.D.

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Mon 8:00–9:50 M4,01024
- Timetable of Seminar Groups:

*V. Horská* **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**- Applied Mathematics for Multi-Branches Study (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Statistics and Data Analysis (programme PřF, N-MA)

**Course objectives**- The main goal of the course is to become familiar with some basic principles of testing statistical hypotheses base on Wald principle, likelihood and score principle connecting the statistical theory with MC simulations, implementation in R, geometry, and statistical graphics for continuous data; to understand and explain basic principles of parametric statistical inference for continuous data; to implement these techniques into R language; to be able to apply them to real data.
**Learning outcomes**- Student will be able:

- to understand principles of likelihood and statistical inference for continuous data;

- to select suitable probabilistic and statistical model in statistical inference for continuous data;

- to build up and explain suitable simulation study for selected statistical test or confidence interval for continuous data;

- to build up and explain suitable statistical test for continuous data;

- to apply statistical inference on real continuous data;

- to implement methods of statistical inference for continuous data in R. **Syllabus**- probabilistic and statistical model,
- likelihood function and its maximisation,
- basic principles of testing statistical hypotheses,
- types of test statistics,
- principles of MC simulations for testing statistical hypotheses,
- design in one-, two-, and multi-sample experiments,
- design in linear regression models for continuous data

**Literature**- KATINA, Stanislav, Miroslav KRÁLÍK and Adéla HUPKOVÁ.
*Aplikovaná štatistická inferencia I. Biologická antropológia očami matematickej štatistiky (Applied statistical inference I)*. 1. vyd. Brno: Masarykova univerzita, 2015. 320 pp. ISBN 978-80-210-7752-2. info - COX, D. R.
*Principles of statistical inference*. 1st ed. Cambridge: Cambridge University Press, 2006. xv, 219. ISBN 0521685672. info - CASELLA, George and Roger L. BERGER.
*Statistical inference*. 2nd ed. Pacific Grove, Calif.: Duxbury, 2002. xxviii, 66. ISBN 0534243126. info

*recommended literature*- KATINA, Stanislav, Miroslav KRÁLÍK and Adéla HUPKOVÁ.
**Teaching methods**- Lectures 2 hours per week.

Practicals 2 hours per week.

On-line using MS Teams or full-time 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
**Follow-Up Courses****Further comments (probably available only in Czech)**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses****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 (Autumn 2020, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2020/M7986