> 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 > Resent-From: [EMAIL PROTECTED] > X-Mailing-List: <[EMAIL PROTECTED]> archive/latest/3615 > X-Loop: [EMAIL PROTECTED] > Resent-Sender: [EMAIL PROTECTED] > > 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