1/ Pearl & MacKenzie had a great simplification of Berkson's paradox in The Book of Why. Skip thinking about hospitals. Instead, flip two coins 100 times but only keep the ones that have at least one heads.
4/ Most statistically trained people think, well, I can sample infinitely, so I'll recover the bias. Or, they'll say, I'll sample "enough" for a good bound. But, you don't need to do that.
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5/ Instead, you flip in (synthetic) pairs. HT => 1 TH => 0 For HH and TT, you ignore the observation. (You must flip in chunks of two. You can't "slide" the window.) Since P(HT) = P(TH), they're equally likely. You have uniformly random bits without estimation.
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6/ In the Berkson example, you induce a unwanted (spurious) dependence. In the (Von Neumann) randomness extractor example, you induce a desirable one!
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