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Are there any approaches of converting a shape that covers a small amount of area to a different shape, rejection sampling on this new shape and mapping the results back to the original shape? I guess I'm just wondering if something like that would work in practice, or if that's what you meant by warping the random variables


What would be a good way to sample along with the spinning shape?


Can we combine rejection sampling with inversion in cases where it is hard to find the inverse of the region?


How do you find a warping function that maps the unit square to any arbitrary region?


To "warp" the random variable, is the general idea to apply the same function for the region on the random variable? How is it different from the approach where we take the inverse of cdf?


Is there a way we could nudge the rejected values slightly to have them land on the sample? This would be an approximation still but would improve the yield.


Could we assign certain rejected areas to still represent a point within the sample? Then there wouldn't be such a high rejection probability.


what's the best way to find a warping function?


If we're just given some probability distribution, is there a way to determine if rejection sampling is a good idea? It seems like we'd need to find out the area in the bounding box by integrating, which is what we were trying to do in the first place?


Are there any better way to do this? Just curious.


For a function like this, would it work to randomly select (all but) one of the variables, determine the range(s) of possible values for any of the missing ones, then uniformly select from those ranges?


Could we use the technique we talked about many lectures ago where we divide this square into smaller squares, do some sampling to see which squares contain part of the swirl and which probably don't, and then do more sampling on the ones that do contain part of the swirl? I might be remembering the specific technique incorrectly but this seemed like the main idea of it...


What sort of transformation would you do to achieve such a warp? Is it a linear transformation?


How do you find the warp transformation? And how do you decide what is a good enough fraction to do rejection sampling?


how to we find the warping function efficiently?