A probability weighting method estimates quantities under a target distribution by generating outcomes from a joint distribution, assigning each sample a target-distribution weight, and using weighted Monte Carlo averages. It avoids the inefficiency of generating many samples only to discard those that fail a rare condition. section 2.2.5
The method connects three operational steps:
- Generate outcomes from the joint probability distribution. section 2.2.5
- Weight outcomes according to their probability in the target distribution. section 2.2.5
- Estimate expectations through weighted averaging, using Monte Carlo estimation. section 2.2.5 section 2.5
Rare conditional outcomes
When estimating a quantity conditional on Y=3, direct simulation may generate many joint samples and retain only those with Y=3. Probability weighting instead supports inference through weighted samples, avoiding the waste caused by rare outcomes. Importance sampling and inverse probability reweighting are named variants; inverse probability reweighting is used in causal inference. section 2.2.5
