SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Simulation Methods - NMST535
Title in English: Simulační metody
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
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
Annotation -
Last update: T_KPMS (15.05.2013)
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.
Aim of the course -
Last update: T_KPMS (15.05.2013)

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.

Course completion requirements - Czech
Last update: prof. RNDr. Jaromír Antoch, CSc. (01.03.2018)

Zkouška je písemná a má ukázat schopnost simulovat nestandardní úlohy. Úloha pro zápočet je též písemná a je zpravidla spojena s úlohou pro zkoušku.

Literature - Czech
Last update: T_KPMS (15.05.2013)

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.

Teaching methods -
Last update: T_KPMS (15.05.2013)

Lecture+exercises.

Requirements to the exam - Czech
Last update: RNDr. Jitka Zichová, Dr. (05.03.2018)

Zkouška je písemná a má ukázat schopnost simulovat nestandardní úlohy.

Syllabus -
Last update: T_KPMS (15.05.2013)

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.

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

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

 
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