Importance Sampling

Importance sampling is a technique used in statistics to estimate the properties of a difficult-to-sample distribution by instead sampling from a more manageable distribution. Imagine you're trying to understand how often a rare event occurs in a complex system. Instead of waiting for that rare event to happen naturally, importance sampling involves intentionally focusing on scenarios where the event is more likely, then adjusting the results to reflect the original odds. This approach makes estimating rare or complex behaviors more efficient and accurate without needing an impractically large number of samples.