Importance Sampling
Importance sampling is a statistical technique used to estimate properties of a target distribution by sampling from a different, more tractable proposal distribution and reweighting the samples. It is particularly useful in Monte Carlo methods for rare event simulation, Bayesian inference, and high-dimensional integration where direct sampling is inefficient or infeasible. The method reduces variance in estimates by focusing computational effort on regions of high importance.
Developers should learn importance sampling when working on problems involving probabilistic models, such as in machine learning for Bayesian neural networks or reinforcement learning, and in scientific computing for simulating rare events like financial risk or particle physics. It is essential for improving the efficiency of Monte Carlo simulations in high-dimensional spaces, where naive sampling would require prohibitively many samples to achieve accurate results.