Bayesianism (Was: Optimal Prediction)

From: Wei Dai <weidai.domain.name.hidden>
Date: Fri, 29 Mar 2002 09:25:24 -0800

On Thu, Mar 28, 2002 at 01:27:18PM -0500, Bill Jefferys wrote:
> I think that if this is the issue then we are looking at different
> interpretations of "predictive power", as I said. My POV is Bayesian.
> I am not thinking in terms of what you can say about ensembles of
> universes, but about what you can predict about *this* universe,

This mailing list was created for the discussion of the idea that all
possible universes exist. It's pretty much a given for all discussion
here.

It's not clear to me that Bayesianism makes sense in this context.
Suppose you live in a single determinstic universe where all of the
initial conditions are known exactly and with certainty. Probability
theory would seem to play no role in this case (except possibly to handle
uncertainty caused by computational limitations, but that's not part of
standard Bayesianism so let's ignore it for now). Living in an ensemble of
all possible universes is similar, because there is no uncertainty other
than those introduced by computational limitations. And again ignoring
those limitations, you know certainly and exactly what effects your
potential actions would have on the multiverse, so you don't need
probability theory to make decisions.

Of course in reality we do face uncertainties caused by computational
limitations, but can probability theory be applied to them in a
principled way? For example does it make sense to assign probabilities to
mathematical conjectures? If so how?

BTW, have you read any of the literature on algorithmic complexity theory
and the closely related theory of inductive inference that Juergen
mentioned? I think it's central to understanding Ockham's razor in a
Bayesian context, but your paper on Ockham's Razor and Bayes' theorem
doesn't seem to cite any of it.
Received on Fri Mar 29 2002 - 09:29:45 PST