Accept-Reject Sampling

Idea is that we have some f(x) that we want to sample from but that’s hard to simulate. What we instead do is sample from another distribution (say a normal) which is easy and then accept points probabilistically. Note that our proposal function p(x) must cover f(x).

The intuition here is say you have some distribution CDF, you can just throw darts on a board and then take the ones which land inside as your best guess of it. Of course, rather than a rectangular board, it would make more sense to have your proposal function be as close to the real function as possible so most points are accepted.

Note for later: add drawings from notes. Also any c or k scaling term is all the same and is meant to make the proposal function cover the real function for all x values.

TODO: Include drawings to demonstrate this concept a bit more.