Selected statistical Methods

Garant předmětu:

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, multivariate 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 of discrete distributions

6. Application of entropy in coding theory

7. Entropy of continuous distributions

8. Summary of basic notions of statistics

9. Paired and Two-sample T-test,

10. Goodness of fit tests,

11. Independence testing, contingency tables

12. Estimation of PDF and CDF

13. Gaussian mixtures and EM algorithm

14. Random processes - stationarity

15. Random processes - examples (Gaussian, Poisson)

16. Memory-less distributions, exponential race

17. Discrete-time Markov chains - introduction

18. Discrete-time Markov chains - classification of states

19. Discrete-time Markov chains - stationarity

20. Discrete-time Markov chains - estimation of parameters

21 MCMC

22. Continuous time Markov chains - introduction

23. Continuous time Markov chains - Kolmogorov equations

24. Queuing theory, Little's theorem

25. Queuing systems M/M/1 and M/M/m

26. Queuing systems M/G/infinity

Syllabus of tutorials:

1. Review 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 of PDF and CDF

8. Random processes, Poisson process

9. Discrete-time Markov chains - stationarity

10. Discrete-time Markov chains - classification of states

11. Exponential race

12. Continuous-time Markov chains

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 practice.

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/NIE-VSM/

No time-table has been prepared for this course

The course is a part of the following study plans:

• Master specialization Software Engineering, in English, 2021 (compulsory course in the program)
• Master specialization Computer Security, in English, 2021 (compulsory course in the program)
• Master specialization Computer Systems and Networks, in English, 2021 (compulsory course in the program)
• Master specialization Design and Programming of Embedded Systems, in English, 2021 (compulsory course in the program)
• Master specialization Computer Science, in English, 2021 (compulsory course in the program)
• Master Specialization Digital Business Engineering, 2023 (compulsory course in the program)