Importance Sampling: Change of Variable

This lecture covers the concept of importance sampling through a change of variable, aiming to speed up Monte Carlo calculations by finding a new integration variable for smoother function evaluation. It explains rewriting integrals, properties of the weight function, and provides examples with and without importance sampling. The lecture also discusses the idea of changing random distributions and the impact on stochastic estimates, along with the scaling of importance sampling with dimension, showcasing the variance ratio with and without importance sampling.