Statistics for Informatics

Lecturer:

Tutor:

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:

• Master branch Knowledge Engineering, in Czech, 2016-2017 (compulsory course in the program)
• Master branch Computer Security, in Czech, 2016-2019 (compulsory course in the program)
• Master branch Computer Systems and Networks, in Czech, 2016-2019 (compulsory course in the program)
• Master branch Design and Programming of Embedded Systems, in Czech, 2016-2019 (compulsory course in the program)
• Master branch Web and Software Engineering, spec. Info. Systems and Management, in Czech, 2016-2019 (compulsory course in the program)
• Master branch Web and Software Engineering, spec. Software Engineering, in Czech, 2016-2019 (compulsory course in the program)
• Master branch Web and Software Engineering, spec. Web Engineering, in Czech, 2016-2019 (compulsory course in the program)
• Master program Informatics, unspecified branch, in Czech, version 2016-2019 (compulsory course in the program)
• Master branch System Programming, spec. System Programming, in Czech, 2016-2019 (compulsory course in the program)
• Master branch System Programming, spec. Computer Science, in Czech, 2016-2017 (compulsory course in the program)
• Master branch Knowledge Engineering, in Czech, 2018-2019 (compulsory course in the program)