From what I understand, SIR is a mechanism for sampling from a distribution $p$ that works as follows:
- Approximate a target distribution $p$ using an importance sample $S$ from a proposal distribution $q$
- Draw a small sample $S_\text{small}$ from $S$ with replacement according to $p$
The result, $S_\text{small}$, is a sample from $p$.
- Why use a small subset and not the full sample $S$ in 1?
- Why is this a variance reduction technique, and why does it matter to reduce the variance?