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Simulation Methods and Statistics - NSTP172

Title:	Simulační metody a statistika
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2017
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Jaromír Antoch, CSc.
Class:	DS, pravděpodobnost a matematická statistika DS, ekonometrie a operační výzkum
Classification:	Informatics > Software Applications Mathematics > Probability and Statistics
Interchangeability :	NMST535
Is incompatible with:	NMST535
Is interchangeable with:	NMST535

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KPMS (17.05.2004)

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: G_M (05.06.2008)

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.

Literature - Czech

Last update: T_KPMS (06.02.2007)

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: G_M (27.05.2008)

Lecture+exercises.

Syllabus -

Last update: T_KPMS (17.05.2004)

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.