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.
3/ I like this example because you can hook it into a similar cool procedure. Say you want a sequence of uniformly random bits. To generate them, you must use a coin that I give you. The coin is biased but, I won't tell you how it's biased. How do you generate the sequence?
-
-
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.
Show this thread -
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.
Show this thread -
6/ In the Berkson example, you induce a unwanted (spurious) dependence. In the (Von Neumann) randomness extractor example, you induce a desirable one!
Show this thread
End of conversation
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.