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.
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.