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othercriteria comments on Probability puzzle - Less Wrong Discussion
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Comments (26)
Please clarify your setup. I'm almost certain that you don't want to put a uniform distribution over the "heads:tails ratios" covering (0, +∞). Rather you mean a uniform distribution of the heads probability over (0, 1), right?
Considering that a uniform distribution on (0, +∞) does not exist, I find this very likely.
Well, you could use an improper prior. The measure exists, it just isn't a probability measure. The prior is over the ratio of heads to tails, which is a postitive, unbounded real valued number, so U(0,1) is certainly not appropriate. However, this is certainly not the prior you would use for the correct Bayesian calculation, though it may be useful as an approximation.
I'm with the intuitivists, sort of. Do the problem for a uniform distribution on (0,1000000) and (0,1000000000) and if the answers are really close to each other, you win.
Yeah, if the distribution looked anything like that the answer would just be N=1, bet heads. So in the interest of interesting problems, it should be interpreted as an uniform distribution over P(heads).