Statistics for Informatics

Lecturer:

Pavel Hrabák (guarantor), Daniel Vašata (guarantor)

Tutor:

Pavel Hrabák (guarantor), Petr Novák (guarantor), Daniel Vašata (guarantor), Jitka Hrabáková, Michal Kupsa

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:

Further information:

https://courses.fit.cvut.cz/MI-SPI/

No time-table has been prepared for this course

The course is a part of the following study plans:

• Knowledge Engineering, in Czech, Presented in Czech, Version 2016 and and 2017 (compulsory course in the program)
• Computer Security, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
• Computer Systems and Networks, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
• Design and Programming of Embedded Systems, in Czech, Version 2016 to 2019 (compulsory course in the program)
• Specialization Web and Software Engineering, in Czech, Version 2016 to 2019 (compulsory course in the program)
• Specialization Software Engineering, in Czech, Version 2016 to 2019 (compulsory course in the program)
• Specialization Web Engineering, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
• Master Informatics, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
• Specialization System Programming, Presented in Czech, Version 2016 to 2019 (compulsory course in the program)
• Specialization Computer Science, Presented in Czech, Version 2016-2017 (compulsory course in the program)
• Knowledge Engineering, in Czech, Presented in Czech, Version 2018 to 2019 (compulsory course in the program)