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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

Selected statistical Methods

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Code Completion Credits Range Language
NI-VSM Z,ZK 7 4P+2C Czech
Garant předmětu:
Pavel Hrabák
Lecturer:
Pavel Hrabák
Tutor:
Pavel Hrabák, Jitka Hrabáková, Petr Novák, Jana Vacková
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:

Basics of probability and statistics, multivariable 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 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:

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:

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/
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
roomTK:BS
Hrabák P.
14:30–16:00
(lecture parallel1)
Dejvice
NTK Ballingův sál
Tue
roomT9:346
Hrabák P.
12:45–14:15
(lecture parallel1
parallel nr.101)

Dejvice
NBFIT učebna
roomT9:346
Hrabák P.
14:30–16:00
(lecture parallel1
parallel nr.102)

Dejvice
NBFIT učebna
Wed
roomTH:A-1442
Hrabáková J.
07:30–09:00
(lecture parallel1
parallel nr.103)

Thákurova 7 (budova FSv)
roomTH:A-1442
Hrabáková J.
09:15–10:45
(lecture parallel1
parallel nr.104)

Thákurova 7 (budova FSv)
roomTH:A-1442
Hrabáková J.
11:00–12:30
(lecture parallel1
parallel nr.105)

Thákurova 7 (budova FSv)
Thu
roomT9:155
Hrabák P.
14:30–16:00
(lecture parallel1)
Dejvice
Posluchárna
Fri
roomTH:A-1242
Vacková J.
11:00–12:30
(lecture parallel1
parallel nr.107)

Thákurova 7 (budova FSv)
roomTH:A-1242
Vacková J.
12:45–14:15
(lecture parallel1
parallel nr.108)

Thákurova 7 (budova FSv)
roomTH:A-1242
Vacková J.
14:30–16:00
(lecture parallel1
parallel nr.109)

Thákurova 7 (budova FSv)
The course is a part of the following study plans:
Data valid to 2024-05-22
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6098106.html