Selected statistical Methods
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| NIE-VSM | Z,ZK | 7 | 4P+2C | English |
- Garant předmětu:
- Pavel Hrabák
- Lecturer:
- Petr Novák
- Tutor:
- Petr Novák
- Supervisor:
- Department of Applied Mathematics
- Synopsis:
-
Summary of probability theory;
Multivariate normal distribution;
Entropy and its application to coding;
Statistical tests: T-tests, goodness of fit tests, independence test;
Random processes - stacionarity;
Markov chains and limiting properties;
Queuing theory
- Requirements:
-
Basics of probability and statistics, multivariate calculus, and linear algebra.
- Syllabus of lectures:
-
1. Summary of basic terms of probability theory
2. Random variables
3. Random vectors
4. Multivariate normal distribution
5. Entropy of discrete distributions
6. Application of entropy in coding theory
7. Entropy of continuous distributions
8. Summary of basic notions of statistics
9. Paired and Two-sample T-test,
10. Goodness of fit tests,
11. Independence testing, contingency tables
12. Estimation of PDF and CDF
13. Gaussian mixtures and EM algorithm
14. Random processes - stationarity
15. Random processes - examples (Gaussian, Poisson)
16. Memory-less distributions, exponential race
17. Discrete-time Markov chains - introduction
18. Discrete-time Markov chains - classification of states
19. Discrete-time Markov chains - stationarity
20. Discrete-time Markov chains - estimation of parameters
21 MCMC
22. Continuous time Markov chains - introduction
23. Continuous time Markov chains - Kolmogorov equations
24. Queuing theory, Little's theorem
25. Queuing systems M/M/1 and M/M/m
26. Queuing systems M/G/infinity
- Syllabus of tutorials:
-
1. Review lesson: basics of probability
2. Random vectors, multivariate normal distribution
3. Entropy and coding theory
4. Entropy, mutual information
5. T-tests
6. Goodness of fit tests, independence test
7. Estimation of PDF and CDF
8. Random processes, Poisson process
9. Discrete-time Markov chains - stationarity
10. Discrete-time Markov chains - classification of states
11. Exponential race
12. Continuous-time Markov chains
13. Queuing theory
- Study Objective:
-
The goal of the course is to introduce to the students advanced probabilistic and statistical methods used in information technology practice.
- Study materials:
-
1. Cover, T. M. - Thomas, J. A. : Elements of Information Theory (2nd Edition). Wiley, 2006. ISBN 978-0-471-24195-9.
2. Durrett, R. : Essentials of Stochastic Processes. Springer, 1999. ISBN 978-0387988368.
3. Grimmett, G. - Stirzaker, D. : Probability and Random Processes (3rd Edition). Oxford University Press Inc., 2001. ISBN 978-0-19-857222-0.
- Note:
- Further information:
- https://courses.fit.cvut.cz/NIE-VSM/
- Time-table for winter semester 2023/2024:
- Time-table is not available yet
- Time-table for summer semester 2023/2024:
-
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri - The course is a part of the following study plans:
-
- Master specialization Software Engineering, in English, 2021 (compulsory course in the program)
- Master specialization Computer Security, in English, 2021 (compulsory course in the program)
- Master specialization Computer Systems and Networks, in English, 2021 (compulsory course in the program)
- Master specialization Design and Programming of Embedded Systems, in English, 2021 (compulsory course in the program)
- Master specialization Computer Science, in English, 2021 (compulsory course in the program)
- Master Specialization Digital Business Engineering, 2023 (compulsory course in the program)