What are variance reduction techniques?

So-called variance reduction techniques reduce Mean Standard Error by decreasing Variance in the numerator of Equation (C. 1) and can be used to speed up simulations by achieving a specified level of precision with a smaller number of Trials.

What kind of methods could be use to reduce variation in Monte Carlo?

The main ones are common random numbers, antithetic variates, control variates, importance sampling, stratified sampling, moment matching, conditional Monte Carlo and quasi random variables.

What is antithetic sampling?

Antithetic sampling reduces the variance of a Monte Carlo estimator by drawing correlated, rather than in- dependent, samples. Instead of computing the exact expectation, Monte Carlo estimators draw samples from the underlying distri- bution and use them to compute an empirical mean.

What is a Monte Carlo study?

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle.

How are antithetic variates used to reduce variance?

The method of antithetic variates attempts to reduce variance by introducing negative correlation between pairs of observations. Example 1 Let U be uniformly distributed over [0,1] then 1 − U is also uniformly distributed over [0,1]. Hence, if we generate a path using as inputs U 1,U 2,…,U nand we generate a second path using 1 − U 1,1 − U

How are antithetic variates used in Monte Carlo methods?

Jump to navigation Jump to search. In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Considering that the error reduction in the simulated signal (using Monte Carlo methods) has a square root convergence, a very large number of sample paths is required to obtain an accurate result.

How does IAND 1 − U iForm reduce variance?

iand 1 − U iform an antithetic pairs in the sense that a large value of one is accompanied by a small value of the other. This suggests that an unusually large or small output computed from the first path is balanced off by the value computed from the antithetic path, resulting in a reduction in variance.