From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon Jul 07 2003 - 21:09:00 MDT
Dan writes
> Mitchell Porter wrote:
>
> > But what I still don't get is what's wrong with 'orthodox statistics'. I
> > obtained my p1/(p1+p2) through frequentist thinking, which is supposed
> > to be anathema to Bayesians.
and what Dan did not quote
> For the red-majority barrel, the probability of
> drawing a red each time is 3/4, blue 1/4; so
> the odds of 3 blues, 7 reds is p1 = (1^3)*(3^7)/(4^10).
> For the blue-majority barrel, it's p2 = (3^3)*(1^7)/(4^10).
> Therefore the overall probability (conditioning
> on the 50-50 prior) is the average of those two
> probabilities. A posteriori we know that this is
> what happened, so the odds that it was the
> blue-majority barrel are
> p2/(p1+p2) = 27/(27+2187) = 1/82
Well, I get 27/(27+1054). Is that right?
> (I note, for example, that you happened to misread the problem Eliezer
> posed; you solved a perfectly fine problem instead, but not exactly the
> problem as posed. That problem has some handy features that which allow
> you to simplify and solve the problem just a bit faster. [Though I sure
> as hell wouldn't notice them unless I was working on paper.])
Be sure to provide as few hints as possible. :)
Darn. I really mean that. No sarcasm intended! One only learns
these things the hard way. I will cogitate on your "handy features"
awhile. (I'm still thinking of how anyone could solve the problem
in 30 seconds!)
Lee
P.S. I appreciate your efforts at explaining the philosophical
differences.
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