# Re: Optimal Prediction

> From [EMAIL PROTECTED]  Fri Mar 29 07:58:20 2002
> Resent-Date: Fri, 29 Mar 2002 07:58:29 -0800
> Date: Fri, 29 Mar 2002 10:57:49 -0500
> To: [EMAIL PROTECTED]
> From: Bill Jefferys <[EMAIL PROTECTED]>
> Subject: Re: Optimal Prediction
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> At 2:39 PM -0800 3/28/02, Hal Finney wrote:
> >Bill Jefferys, <[EMAIL PROTECTED]>, writes:
> >>  >>  Ockham's razor is a consequence of probability theory, if you look at
> >>  >  > things from a Bayesian POV, as I do.
> >>
> >>  This is well known in Bayesian circles as the Bayesian Ockham's
> >>  Razor. A simple discussion is found in the paper that Jim Berger and
> >>  I wrote:
> >>
> >>    http://bayesrules.net/papers/ockham.pdf
> >
> >This is an interesting paper, however it uses a slightly unusual
> >interpretation of Ockham's Razor.  Usually this is stated as that the
> >simpler theory is preferred, or as your paper says, "an explanation of
> >the facts should be no more complicated than is necessary."  However the
> >bulk of your paper seems to use a different definition, which is that
> >the simpler theory is the one which is more easily falsified and which
> >makes sharper predictions.
> >
> >I think most people have an intuitive sense of what "simpler" means, and
> >while being more easily falsified frequently means being simpler, they
> >aren't exactly the same.  It is true that a theory with many parameters
> >is both more complex and often less easily falsified, because it has more
> >knobs to tweak to try to match the facts.  So the two concepts often do
> >go together.
> >
Bill Jefferys writes, quoting Hal Finney:
> >But not always.  You give the example of a strongly biased coin being
> >a simpler hypothesis than a fair coin.  I don't think that is what
> >most people mean by "simpler".  If anything, the fair coin seems like
> >a simpler hypothesis (by the common meaning) since a biased coin has a
> >parameter to tweak, the degree of bias.
>
> Depends on whether you know the degree of bias. If you are choosing
> between a two-headed coin and a fair coin, the two-headed coin is
> simpler since it can explain only one outcome, whereas a fair coin
> would be consistent with any outcome. On the other hand, if you don't
> know the bias, then between a fair coin and a coin with unknown bias,
> the fair coin is simpler. This automatically pops out when you do the
> analysis.

That's true, but even so, a coin with a .95 chance of coming up heads
and a .05 chance of coming up tails is "simpler" by your definition
than a fair coin, right?  Even though the parameter is not adjustable,
the presence of an ad hoc value like .95 makes it seem intuitively less
simple than a fair coin, at least to me.

Hal Finney