I'm reading a paper about raytracing/integration and there is this step where it argues that two samples from distributions p1 and p2 respectively can be used to produce a sample from a distribution whose pdf is the product of pdfs of p1 and p2. Does that sound plausible?
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Maybe I misunderstand what this is saying but I really can't imagine how this would work for the general case. Consider slightly overlapping "cat ears" distributions:pic.twitter.com/td5PMOClUB
You can make the overlap arbitrarily small and therefore make it arbitrarily unlikely to ever sample anything in pdf3 by sampling pdf1 or pdf2.
