Re: Optimal Prediction

From: Bill Jefferys <bill.domain.name.hidden>
Date: Thu, 28 Mar 2002 13:33:11 -0500

At 6:09 PM +0100 3/28/02, Juergen Schmidhuber wrote:
>
>Predictive power is measurable by standard concepts of probability theory
>and complexity theory.

Agreed.

> You may choose to ignore this, but don't include
>all those who don't among "the rest of us".
>
>Write down all assumptions, derive the consequences, and observe that
>the AP _by itself_ cannot predict anything nontrivial.

If your point is that it cannot predict anything _by itself_ then I
agree. There is always background information, and one is required
(as you say) to make use of whatever background information you may
have.

>Fortunately Hoyle was more careful than some who cite him - he just
>wrote: "the results...were obtained subject to certain assumptions
>...have not been demonstrated in a manner free from all doubt.
>Nevertheless, the number of assumptions made was much less
>than the number of results obtained."
>
>Thus he informally invoked Occam's razor: find short descriptions that
>explain a lot. Occam's razor is not the AP. It is formally treated by
>the theory of inductive inference. Although this theory is at the heart
>of what physicists are doing, some of them are not yet fully aware of
>it.

Ockham's razor is a consequence of probability theory, if you look at
things from a Bayesian POV, as I do.

I regard Hoyle's prediction as a genuine prediction of the
AP+background information that Hoyle had. Do you disagree with that?

I've put you back on my reading list, and I apologize to you for
getting annoyed.

Bill
Received on Thu Mar 28 2002 - 10:37:05 PST