Selected statistical methods
Code  Completion  Credits  Range  Language 

MIVSM  Z,ZK  8  4P+2C  Czech 
 Course guarantor:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Applied Mathematics
 Synopsis:

Summary of probability theory;
Multivariate normal distribution;
Entropy and its application to coding;
Statistical tests: Ttests, 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 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, 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. 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/MISPI/
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Master specialization Computer Science, in Czech, 20182019 (compulsory course in the program)