From: Lee Daniel Crocker (lcrocker@calweb.com)
Date: Wed Mar 26 1997 - 01:39:58 MST
> From what I've read on Bayesian inference, judgements not based on Bayesian
> methods or methods with indistinguishable results are objectively bad. If
> most people are using an objectively inferior inference process, what does
> that do to the value of other people's opinions for a rational Bayesian?
The only judgments where non-Bayesian inferences are "objectively bad"
in your sense are ones that are trivially simple and contrived to fit
the mathematical models exactly. For example, gambling. Let us
imagine a bag filled with red and black balls. We are asked to bet
on whether a ball drawn from the bag will be red or black, but we are
not told beforehand how many of each are in it. After each draw, the
ball is replaced and we make another bet. The conditions of the game
are given and fixed, and our observations are trusted--guarantess that
most of reality doesn't give us. Under these conditions, a bettor
using Bayesian inference to infer the number of red and black balls
will, in the long run, always make more money than someone using any
other method (we are also given that cheating is impossible). Only
in that limited sense is Bayes "ideal", but that tells us little that
is useful; it only tells us that this formula works where we have
defined the conditions for it to work, nothing more.
By what rational means do we apply the precise mathematical model of
Bayes to items in the real world, especially when those items are as
obscenely complex and chaotic as human ideas? Is that foundation any
stronger than our earlier application of the calculus of Newton to the
real world of gravitation, a much simpler mapping? This is just a
dressed-up version of the problem of induction. Why do think induction
works? Because it usually does--an inductive argument. If we are to
judge whether or not Bayesian inference can be applied to certain parts
of the real world, what criteria will we use to judge the evidence? If
you can offer me nothing better than Bayesian inference from that
evidence, then I am unsatisfied.
-- Lee Daniel Crocker <lee@piclab.com> <http://www.piclab.com/lcrocker.html> "All inventions or works of authorship original to me, herein and past, are placed irrevocably in the public domain, and may be used or modified for any purpose, without permission, attribution, or notification."--LDC
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