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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

MI-VSM Selected statistical methods Extent of teaching: 4P+2C
Instructor: Completion: Z,ZK
Department: 18105 Credits: 8 Semester: L

Annotation:
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

Lecture syllabus:
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

Seminar syllabus:
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

Literature:
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.

Requirements:
Basics of probability and statistics, multivariable calculus, and linear algebra.

Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/MI-SPI/

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NI-TI.2018 Computer Science PP 2


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška