Mathematics PS

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Focused on basic and more advanced statistical and probabilistic methods of data analysis as well as on hypothesis testing and regression.

Requirements:

None.

Syllabus of lectures:

1. Descriptive statistics, measures of location and scale, empirical distribution function

2. Simple random sample and ordered sample

3. Normally distributed random variable

4. Correlation, Pearson, and Spearman sample correlation coefficient

5. Principle of statistical hypothesis testing

6. One-sample tests (t-test, F-test, sign (binomial) test, Wilcoxon test)

7. Two-sample tests (two-sample t-test and Wilcoxon test, Kolmogorov-Smirnov test)

8. Linear regression and the least squares method

9. Robust estimates of location and scale

10. Robust estimates in linear regression 1 (Huber, Tukey)

11. Robust estimates in linear regression 2 (LMS, LTS)

12. Classical statistics in R-project

13. Robust statistics in R-project

Syllabus of tutorials:

Exercise class follows the syllabus topics.

Study Objective:

Students wil become familiar with statistical and probabilistic methods of data analysis.

Study materials:

!Jarušková D.: Pravděpodobnost a matematická statistika, Vydavatelství ČVUT, Praha, 2006, ISBN: 978-80-01-04829-0.

!Anděl J.: Statistické metody, Matfyzpress, MFF UK, Praha, 5. vydání, 2019, ISBN 978-80-7378-381-5

?Zvára K., Štěpán J.: Pravděpodobnost a matematická statistika. Matfyzpress, MFF UK, Praha, 6. vydání, 2019, ISBN 978-80-7378-388-4.

?Wasserman L.: All of Statistics: A Concise Course in Statistical Inference. Springer Texts in Statistics, Corr. 2nd printing, Springer, New York, 2010, ISBN 9781441923226

:online https://cmp.felk.cvut.cz/~navara/stat/PMS_ebook.pdf , Navara M.: Pravděpodobnost a matematická statistika. FEL ČVUT, Praha, 2020

Note:

Further information:

Připravuje se.

No time-table has been prepared for this course

The course is a part of the following study plans:

• Stavební inženýrství - pozemní stavby, specializace Projektování pozemních staveb (compulsory course)
• Stavební inženýrství - pozemní stavby, specializace Statika pozemních staveb (compulsory course)