Re: Isn't the Frequentist a subset or special case of Bayesianist?

On Sat, 02 Jul 2005 10:31:52 +0300, "Anon."
<bob.ohara@xxxxxxxxxxxxxxxxx> wrote:
>No, a beta(1,1) does fine.
>
> From <http://mathworld.wolfram.com/BetaDistribution.html>, the pdf of a
>beta is proportional to p^(a-1) (1-p)^(b-1).
>
>For a binomial, with r successes and n trials, the likelihood is
>proportional to p^r (1-p)^(n-r).
>
>The posterior is the product of these, so is proportional to
>
>p^(a+r-1) (1-p)^(b+n-r-1).
>
>If a=b=1, we recover a posterior that's proportional to the likelihood.
> Note that a=b=1 gives a uniform prior.

Except that the mean of p^(r) (1-p)^(n-r) is (r+1)/(n+2) so this would
be a biased estimator for p.
.

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