SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Simulation Methods - NMST535
Title: Simulační metody
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023 to 2023
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: the course is taught as cyclical
Guarantor: prof. RNDr. Jaromír Antoch, CSc.
Class: Pravděp. a statistika, ekonometrie a fin. mat.
M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Informatics > Software Applications
Mathematics > Probability and Statistics
Is interchangeable with: NSTP172
Annotation -
Notion of randomness. Random number generation from uniform distribution, tests of randomness. Methods for generation of random variables from univariate distributions including the normal, gamma, chi-square distributions. Generation from discrete and empirical distributions. Methods for generation from multivariate distibutions including multivariate normal and Dirichlet distributions. Generation of order statistics, random samples, random processes and generation on selected structures. Monte Carlo integration and optimization.
Last update: T_KPMS (15.05.2013)
Aim of the course -

The aim of the lecture is to introduce the students with both basic and advanced methods of stochastic simulations. They will be able to realize simulation studies required in another courses.

Last update: T_KPMS (15.05.2013)
Course completion requirements -

Written exam.

Last update: Zichová Jitka, RNDr., Dr. (02.05.2023)
Literature - Czech

Devroye, L.: Non-uniform random number generation. Springer, 1986.

Robert, Ch. P., Casella, C.: Monte Carlo Statistical Methods. Springer, 2005.

Ross, S.M.: Simulation. Elsevier, 2006.

Last update: T_KPMS (15.05.2013)
Teaching methods -

Lecture+exercises.

Last update: T_KPMS (15.05.2013)
Requirements to the exam -

Written exam -simulations of sofisticated problems.

Last update: Zichová Jitka, RNDr., Dr. (02.05.2023)
Syllabus -

1. Notion of randomness.

2. Random number generation from uniform distribution, tests of randomness.

3. General methods for generation of random variables from univariate distributions

(inversive methods, rejection method, stochastic methods, method of envelope,

ratio of uniforms method, Forsyth method, alias-rejection method, method of

transformation etc.)

4. Specific methods for generation from the normal, gamma, chi-square and analogous

distributions.

5. Generation from discrete and empirical distributions.

6. General methods for generation from multivariate distibutions (rejection method, stochastic

methods, transformation to the independent components etc.)

7. Specific methods for generation from multivariate normal, Dirichlet and other distributions.

8. Generation of order statistics, random samples and generation on selected structures

(sphere, ellipsoid, simplex, trees, graphs etc.)

9. Generation of random processes.

10. Monte Carlo integration and comparison wit standard numerical approach.

11. Monte Carlo optimization.

Last update: T_KPMS (15.05.2013)
Entry requirements -

Random variables and vectors and their characterizations; central limit theorem; conditional distribution; numerical integration.

Last update: Antoch Jaromír, prof. RNDr., CSc. (04.06.2018)
 
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