 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Statistics for Informatics

Code Completion Credits Range Language
MI-SPI.16 Z,ZK 7 4P+2C Czech
Lecturer:
Pavel Hrabák (guarantor), Daniel Vašata
Tutor:
Pavel Hrabák (guarantor), Jitka Hrabáková, Michal Kupsa, Petr Novák, Daniel Vašata
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, 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, independence 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. Shao, J. - Tu, D. The Jackknife and Bootstrap. Springer, 1995. ISBN 978-1-4612-0795-5.

2. Cover, T. M. - Thomas, J. A. Elements of Information Theory (2nd Edition). Wiley, 2006. ISBN 978-0-471-24195-9.

3. Ludeman, L. Random Processes: Filtering, Estimation, and Detection. Wiley{IEEE Press, 2003. ISBN 978-0-471-25975-6.

4. Durrett, R. Essentials of Stochastic Processes. Springer, 1999. ISBN 978-0387988368.

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
 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 roomT9:155Hrabák P.Vašata D.09:15–10:45(lecture parallel1)DejvicePosluchárna roomT9:346Kupsa M.07:30–09:00(lecture parallel1parallel nr.101)DejviceNBFIT učebnaroomTH:A-1442Hrabák P.09:15–10:45(lecture parallel1parallel nr.102)Thákurova 7 (FSv-budova A)roomTH:A-942Kupsa M.11:00–12:30(lecture parallel1parallel nr.103)Thákurova 7 (FSv-budova A)roomT9:343Kupsa M.12:45–14:15(lecture parallel1parallel nr.104)DejviceNBFIT učebna roomTH:A-1442Vašata D.09:15–10:45(lecture parallel1parallel nr.105)Thákurova 7 (FSv-budova A)roomT9:155Hrabák P.Vašata D.11:00–12:30(lecture parallel1)DejvicePosluchárnaroomTH:A-1247Novák P.12:45–14:15(lecture parallel1parallel nr.106)Thákurova 7 (FSv-budova A)seminární místnost roomT9:346Hrabáková J.09:15–10:45(lecture parallel1parallel nr.107)DejviceNBFIT učebnaroomT9:346Hrabáková J.11:00–12:30(lecture parallel1parallel nr.108)DejviceNBFIT učebna
The course is a part of the following study plans:
Data valid to 2020-01-26
For updated information see http://bilakniha.cvut.cz/en/predmet4661406.html