Selected statistical Methods
Code  Completion  Credits  Range  Language 

NIVSM  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 (Ttests, 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 Twosample Ttest,
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. Memoryless 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. Ttests
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 9780471241959.
2. Durrett, R. : Essentials of Stochastic Processes. Springer, 1999. ISBN 9780387988368.
3. Grimmett, G.  Stirzaker, D. : Probability and Random Processes (3rd Edition). Oxford University Press Inc., 2001. ISBN 9780198572220.
 Note:
 Further information:
 https://courses.fit.cvut.cz/NIVSM/
 Timetable for winter semester 2023/2024:
 Timetable is not available yet
 Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans:

 Master specialization Computer Security, in Czech, 2020 (compulsory course in the program)
 Master specialization Design and Programming of Embedded Systems, in Czech, 2020 (compulsory course in the program)
 Master specialization Computer Systems and Networks, in Czech, 202 (compulsory course in the program)
 Master specialization Management Informatics, in Czech, 2020 (compulsory course in the program)
 Master specialization Software Engineering, in Czech, 2020 (compulsory course in the program)
 Master specialization System Programming, in Czech, version from 2020 (compulsory course in the program)
 Master specialization Web Engineering, in Czech, 2020 (compulsory course in the program)
 Master specialization Knowledge Engineering, in Czech, 2020 (compulsory course in the program)
 Master specialization Computer Science, in Czech, 2020 (compulsory course in the program)
 Mgr. programme, for the phase of study without specialisation, ver. for 2020 and higher (compulsory course in the program)
 Master specialization System Programming, in Czech, version from 2023 (compulsory course in the program)
 Master specialization Computer Science, in Czech, 2023 (compulsory course in the program)