> That's exactly it, though.
Ok, so instead of estimating B/A=1/100 just estimate A/B=100. What's the problem with this argument?
Ok, so instead of estimating B/A=1/100 just estimate A/B=100. What's the problem with this argument?
There are situations where you would use rejection sampling because generating 100x more random numbers is much cheaper than doing the complex calculations required to accurately model the space in question. Maybe 50 dimensions (and the 13 orders of magnitude difference) isn't big enough to raise those concerns. If we instead talk about 100 dimensions, then we're dealing with a difference of 40 orders of magnitude, and if you tell me that still doesn't matter, then I don't know what to say.
They're both problems. If you want to estimate 1e1000 via sampling individual points, then you need at least that order of magnitude of samples. If all of your data points fall in one class, then it doesn't matter what you're trying to calculate from that.
As I said: "If you're inverting the ratio we're estimating, then instead of estimating the value at 0, we're estimating it at infinity (or, okay, if you want to use Laplace smoothing, then a million, which is far too low)."
Ok so if the ratio is 1/2 how many samples do you need?
My entire point is that this becomes infeasible very quickly for numbers that are not all that big.
Second, your claim that it depends on dimension is wrong, given the ratio of sets, dimension doesn't matter. If the ratio is 1/2 then you'll reject one half of the times regardless of dimension, and so by your own argument it's "very efficient"