Rejection sampling works reasonably well when its envelope closely bounds the target density, but scales poorly, particularly for high-dimensional data.

“The first idea which kind of came up more or less in the same time was doing something like rejection sampling. So rejection sampling something that you may have already seen like in school where you try where you did like you you uh painted a square, you had a circle inside of it and they did like random points. And then the fraction of random points that is in the circle, you can use that to compute pi. Exactly the same idea you can do with any kind of density as long as you have something we just”

“just kind of above it. Right, let's say we have uh like a just a box which is I have which is essentially an uh a uniform distribution, then you scale it up to be basically around your density, and then you randomly pepper with points.”

“That's rec rejection sampling, and it works pretty well assuming you have uh a relatively close envelope over your function. So it doesn't end up scaling very well, especially with high dimensional data.”