Variance Reduction Techniques: Antithetic Variables & Importance Sampling

This lecture introduces variance reduction techniques to improve the Monte Carlo estimator, focusing on antithetic variables and importance sampling. By constructing new random variables with the same mean but smaller variance, these techniques aim to reduce the error in estimation. Antithetic variables involve generating negatively correlated pairs of random variables, while importance sampling aims to improve the constant in the error bound by reducing the variance of the estimator. The instructor explains how to apply these techniques in practice, using examples like random walks and stochastic simulations. By leveraging the properties of symmetric distributions and monotonic functions, these methods can lead to significant variance reduction in Monte Carlo simulations.