Course details

# Statistics and Probability

MSP Acad. year 2021/2022 Winter semester 5 credits

Summary of elementary concepts from probability theory and mathematical statistics. Limit theorems and their applications. Parameter estimate methods and their properties. Scattering analysis including post hoc analysis. Distribution tests, tests of good compliance, regression analysis, regression model diagnostics, non-parametric methods, categorical data analysis. Markov decision-making processes and their analysis, randomized algorithms.

Guarantor

Course coordinator

Language of instruction

Czech

Completion

Credit+Examination (written)

Time span

• 26 hrs lectures
• 21 hrs exercises
• 5 hrs projects

Assessment points

• 70 pts final exam (written part)
• 20 pts mid-term test (written part)
• 10 pts projects

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

Students will extend their knowledge of probability and statistics, especially in the following areas:

• Parameter estimates for a specific distribution
• simultaneous testing of multiple parameters
• hypothesis testing on distributions
• regression analysis including regression modeling
• nonparametric methods
• Markov processes
• randomised algorithms

Learning objectives

Introduction of further concepts, methods and algorithms of probability theory, descriptive and mathematical statistics. Development of probability and statistical topics from previous courses. Formation of a stochastic way of thinking leading to formulation of mathematical models with emphasis on information fields.

Why is the course taught

The society development desires also technology and, in particular, information technology expansion. It is necessary to process information - data in order to control technology. Nowadays, there is a lot of devices that collect data automatically. So we have a large amount of data that needs to be processed. Statistical methods are one of the most important means of processing and sorting data, including their analysis. This allows us to obtain necessary information from your data to evaluate and control.

Prerequisite knowledge and skills

Foundations of differential and integral calculus.

Foundations of descriptive statistics, probability theory and mathematical statistics.

Study literature

• Anděl, Jiří. Základy matematické statistiky. 3.,  Praha: Matfyzpress, 2011. ISBN 978-80-7378-001-2.
• FELLER, W.: An Introduction to Probability Theory and its Applications. J. Wiley, New York 1957. ISBN 99-00-00147-X
• Hogg, V.R., McKean J.W. and Craig A.T. Introduction to Mathematical Statistics. Seventh Edition, 2012. Macmillan Publishing Co., INC. New York. ISBN-13: 978-0321795434  2013
• Zvára K.. Regresní analýza, Academia, Praha, 1989
• Meloun M., Militký J.: Statistické zpracování experimentálních dat (nakladatelství PLUS, 1994).
• D. P. Bertsekas, J. N. Tsitsiklis. Introduction to Probability, Athena, 2008. Scientific

Syllabus of lectures

1. Summary of basic theory of probability and random variables: axiomatic definition of probability, conditional probability, discrete and continuous random variable, significant probability distributions, random vector.
2. Summary of basic methods in statistics: parameter estimate, hypothesis testing, goodness-of-fit tests, regression analysis - regression line.
3. Extension of hypothesis tests for binomial and normal distributions.
4. Analysis of variance (simple sorting, ANOVA), post hos analysis
5. Analysis of categorical data. Contingency table. Independence test. Four-field tables. Fisher's exact test.
6. Project assignment, demonstration of the use of statistical tools (programs) for solving the project and other statistical tasks.
7. Regression analysis. Creating a regression model. Testing hypotheses about regression model parameters. Comparison of regression models. Diagnostics.
8. Distribution tests.
9. Nonparametric methods of testing statistical hypotheses - part 1.
10. Nonparametric methods of testing statistical hypotheses - part 2.
11. Markov processes and their analysis.
12. Markov decision processes and their basic analysis.
13. Introduction to randomized algorithms and their use (Monte Carlo, Las Vegas, applications).

Syllabus of numerical exercises

1. Summary of basic theory of probability and random variables.
2. Summary of basic methods in statistics.
3. Hypothesis tests for binomial and normal distributions.
4. Analysis of variance, sorting, post host analysis.
5. Analysis of categorical data. Contingency table. Four-field tables.
6. Demonstration of the use of statistical tools (programs).
7. Regression analysis.
8. Tests on distribution, tests of good agreement.
9. Nonparametric methods of testing statistical hypotheses - one-sample.
10. Nonparametric methods of testing statistical hypotheses - two or more sample ones.
11. Application and analysis of Markov processes.
12. Basic application and analysis of Markov decision processes.
13. Design and analysis of basic randomised algorithms.

Syllabus - others, projects and individual work of students

1.  Usage of tools for solving statistical problems (data processing and interpretation).

Progress assessment

Three tests will be written during the semester - 6th and 11th week. The exact term will be specified by the lecturer. The test duration is 60 minutes. The evaluation of each test is 0-10 points.

Projected evaluated 0-10 points.

Final written exam - 60 points

Controlled instruction

Participation in lectures in this subject is not controlled

Participation in the exercises is compulsory. During the semester two abstentions are tolerated. Replacement of missed lessons is determined by the leading exercises.

Exam prerequisites

Fulfil the attendance conditions and achieve in total at least 15 points from the tests and the project.

Course inclusion in study plans