Selected statistical Methods
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
NI-VSM | Z,ZK | 7 | 4P+2C | Czech |
- Garant předmětu:
- Lecturer:
- Tutor:
- Supervisor:
- Department of Applied Mathematics
- Synopsis:
-
The course leads the student through advanced probabilistic and statistical methods used in information technology praxis. Particularly it deals with multivariate normal distribution, application of entropy in coding theory, hypothesis testing (T-tests, goodness of fit tests, independence test). Second part of the course deals with random processes with focus on Markov chains. The high point of the course is the Queuing theory and its application in networks.
- Requirements:
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Basics of probability and statistics, multivariable calculus, and linear algebra.
- Syllabus of lectures:
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1. Summary of basic terms of probability theory
2. Random variables
3. Random vectors
4. Multivariate normal distribution
5. Entropy for discrete distribution
6. Application of entropy in coding theory
7. Entropy of continuous distribution
8. Summary of basic terms of statistics
9. Paired and Two-sample T-test,
10. Goodness of fit tests,
11. Independence test, contingency table
12. Estimation od PDF and CDF
13. Gaussian mixtures and EM algorithm
14. Random processes - stacionarity
15. Random processes - examples (Gaussian, Poisson)
16. Memory-less distributions, exponential race
17. Markov chain with discrete time
18. Markov chain with discrete time - state classiffication
19. Markov chain with discrete time - stationarity
20. Markov chain with discrete time - parameters estimation
21 MCMC
22. Markov chain with continuous time
23. Markov chain with continuous time - Kolmogorov equations
24. Queuing theory, Little theorem
25. Queuing systems M/M/1 and M/M/m
26. Queuing systems M/G/infty
- Syllabus of tutorials:
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1. Revision 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, sndependence test
7. Estimation od PDF and CDF
8. Random processes, Poisson
9. Markov chain with discrete time - stationarity
10. Markov chain with discrete time - state classiffication
11. Exponential race
12. Markov chain with continuous time
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 praxis.
- Study materials:
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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/NI-VSM/
- No time-table has been prepared for this course
- The course is a part of the following study plans:
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- Master specialization Computer Security, in Czech, 2020 (compulsory course in the program)
- Master specialization Design and Programming of Embedded Systems, in Czech, 2020 (compulsory course in the program)
- Master specialization Computer Systems and Networks, in Czech, 202 (compulsory course in the program)
- Master specialization Management Informatics, in Czech, 2020 (compulsory course in the program)
- Master specialization Software Engineering, in Czech, 2020 (compulsory course in the program)
- Master specialization System Programming, in Czech, version from 2020 (compulsory course in the program)
- Master specialization Web Engineering, in Czech, 2020 (compulsory course in the program)
- Master specialization Knowledge Engineering, in Czech, 2020 (compulsory course in the program)
- Master specialization Computer Science, in Czech, 2020 (compulsory course in the program)
- Mgr. programme, for the phase of study without specialisation, ver. for 2020 and higher (compulsory course in the program)
- Master specialization System Programming, in Czech, version from 2023 (compulsory course in the program)
- Master specialization Computer Science, in Czech, 2023 (compulsory course in the program)