"Computing distributional overlap out in the tails of high dimensional
distributions…   Seems like it couldn’t possibly be sampled well
enough to be informative."

But isn't that where the money is? It is this kind of sampling game
with limited resources over ridiculously large spaces that some of the
worlds largest investments get funneled into. The idea often is to get
better sketches of distributions, spending as little time resampling
the deepest wells.
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