RE: More Hard Problems Using Bayes' Theorem, Please

From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon Jul 07 2003 - 21:09:00 MDT

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    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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