Importance Sampling — Variance Reduction for Rare Events

Importance sampling is a Monte Carlo variance-reduction technique that shifts the sampling distribution toward the region of interest — typically a rare or extreme event — so that informative samples are drawn far more often than under the original distribution. Developed at the RAND Corporation by Herman Kahn and Theodore Harris around 1951, it makes tail-probability estimation (such as Value-at-Risk or system-failure probability) tractable where standard Monte Carlo would require an astronomically large number of runs.