Lecture 4 Variance reduction methods
Antithetic variables
Control variable
Conditional Monte Carlo
Stratification
References:
Jack P.C. Kleijnen, Ad A.N. Ridder & Reuven Rubinstein, Variance reduction
techniques in Monte Carlo methods, in Encyclopedia of
Lecture 3 Random variable generation (2)
Rejection sampling (general case)
Example: generating Z~ N(0,1)
Efficiency = 76%
Example: Generating truncated normal
Let
We want to draw from the following density
It is natural to use the normal as trial density
Lecture 2: Random variable generation
Random number generation
Inverse-transformation method
Sampling from finite distribution
Acceptance-Rejection method
Composition method
Lecture 2: random number generation
Generating random numbers in cfw_0, 1,
,