On Mon, Apr 15, 2002 at 04:15:32PM +0200, Juergen Schmidhuber wrote:
For example, suppose the process computing the universe is not optimally
efficient for some reason. As long as the resource postulate holds the
true prior cannot dominate the Speed Prior, and S-based predictions
will be
Wei Dai wrote:
BTW, isn't the justification for universal prediction taken in this paper
kind of opposite to the one you took? The abstract says The problem,
however, is that in many cases one does not even have a reasonable guess
of the true distribution. In order to overcome this problem
Bill Jefferys wrote:
At 10:59 AM +0200 4/3/02, Juergen Schmidhuber wrote:
The theory of inductive inference is Bayesian, of course.
But Bayes' rule by itself does not yield Occam's razor.
By itself? No one said it did. Of course assumptions must be made.
At minimum one always has to choose
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
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
Sorry, I mis-edited that message. Here it is cleaned up for clarity:
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,
At 9:20 AM -0800 3/29/02, Hal Finney wrote:
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
Bill Jefferys wrote:
At 9:20 AM -0800 3/29/02, Hal Finney wrote:
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
Bill Jefferys wrote:
At 9:19 AM +0100 3/27/02, Juergen Schmidhuber wrote:
You are claiming the AP necessarily implies a specific fact about
nuclear energy levels? I greatly doubt that - can you give a proof?
Yes, I can.
Bill Jefferys wrote:
It's pointless wasting my time on this. As both Russell and I pointed
out, this is a standard example that is cited by people who are
knowledgeable about the AP. Either you have a different definition of
predictive power than the rest of us do, or you don't understand
On Thu, Mar 28, 2002 at 10:44:41AM -0500, Bill Jefferys wrote:
It's pointless wasting my time on this. As both Russell and I pointed
out, this is a standard example that is cited by people who are
knowledgeable about the AP. Either you have a different definition of
predictive power than
At 9:32 AM -0800 3/28/02, Wei Dai wrote:
Perhaps you're not familiar with the history of this mailing list, but
Juergen Schmidhuber is one of the first authors to explicitly state the
idea that all possible universes exist in a published scientific paper,
and that paper is cited in the public
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
I don't understand this point.
Bill Jefferys wrote:
Ockham's razor is a consequence of probability theory, if you look at
things from a Bayesian POV, as I do.
Saibal Mitra
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
I agree at this point that the AP by itself has no predictive power. My
view is that a predictor that currently works in a given universe - say the
AP plus other stuff - can not be considered to continue to work. Any
universe is subject to true noise either because its rules allow it [type
My son was taking a class in college on the philosophy of science.
One of the things they talked about was the validity of induction.
The basic idea of induction is to identify a pattern and extrapolate
it forward. Simplified, induction assumes that the way things have been
in the past is the
At 9:19 AM +0100 3/27/02, Juergen Schmidhuber wrote:
Bill Jefferys wrote:
At 2:25 PM +0100 3/26/02, Juergen Schmidhuber wrote:
But unfortunately the anthropic principle does not have any
predictive power. It does NOT predict there won't be any flying
rabbits tomorrow.
But Hoyle did
Juergen Schmidhuber wrote:
Bill Jefferys wrote:
At 2:25 PM +0100 3/26/02, Juergen Schmidhuber wrote:
But unfortunately the anthropic principle does not have any
predictive power. It does NOT predict there won't be any flying
rabbits tomorrow.
But Hoyle did use the AP to
At 2:25 PM +0100 3/26/02, Juergen Schmidhuber wrote:
But unfortunately the anthropic principle does not have any
predictive power. It does NOT predict there won't be any flying
rabbits tomorrow.
But Hoyle did use the AP to predict specific facts about nuclear
energy levels, which were
At 3/26/02, you wrote:
Normally we do not know the true conditional probability
distribution p(next event | past). But assume we do know that
p is in some set P of distributions.
As I posted earlier my issue with this is how does one know p is in P
unless one can compute p, i.e. check it?
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