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comment by mike
mike  ·  944 days ago  ·  link  ·    ·  parent  ·  post: The fake coin probability problem

This is interesting. What do we do in cases when we don't know the selection process? Is there an assumption-less way to proceed? Thorny. And it's going to bother me now...

enginerd  ·  943 days ago  ·  link  ·

We guess. Or use domain specific knowledge, if available. Imagine playing 3-card monte with your friend (who you know has no history of doing card tricks, possibly has learned something knew in the last week but nothing major) versus somebody on the street. You'd assign different probabilities of yourself winning in each case, right?

Say I flip a coin once and you have to guess the face. You ask if the coin is fair. I answer "Unknown". One could assume that it's probably fair, and if it's unfair it's equally likely to be unfair in either direction, in which case it's 0.5 each (for the first flip only).

b_b mentioned Bayesian inference, that's a way to include prior knowledge. But of course people with different prior assumptions will get different answers. So it goes.

b_b  ·  944 days ago  ·  link  ·