Seonglae ChoUsing proxy distribution to sample target distribution .
When we can calculate p values but it's difficult to sample from the entire p distribution
A technique that draws samples from a proposal distribution and determines the final sample based on evaluating the validity of these samples. Only assumption is that you know how to sample a density such that where is a known constant.
- Sample from q
- Sample
- If , accept else go back to 1 (Importance sampling like approach but only for criteria)
On average, iterations needed to obtain one point sampled from . is better to be smaller.
Because the acceptance probability is
on average you need iterations to obtain one accepted samples.
Rejection sampling
In numerical analysis and computational statistics, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance-rejection method or "accept-reject algorithm" and is a type of exact simulation method. The method works for any distribution in
R
m
{\displaystyle \mathbb {R} ^{m}}
with a density.
https://en.wikipedia.org/wiki/Rejection_sampling