From: Ben Goertzel (ben@goertzel.org)
Date: Thu Aug 29 2002 - 16:26:06 MDT
Eliezer wrote:
> > I fail to see why anyone would hold this theorem so highly that he
> > writes poetry about it. In fact, I do not really think that you (Eli)
> > really understand the theorem. For instance, this example is given in
> > my book on elementary probability theory as a direct application of
> > Bayes Th.:
>
> Heh. Well, I am not alone in holding the BPT in very high esteem. There
> is a small but growing movement in science to replace the Popperian view
> of proof with a Bayesian view, and you will often find "Bayesian
> rationalist" used as a more precise synonym for "rationalist", so it's not
> just me.
Of course, you are correct here, Eliezer. "Bayesianism" is a philosophy of
applied modeling which has quite a few true believers. I'm surprised that
Christian has not encountered it before...
Bayesian analysis doesn't simply refer to the use of Bayes Theorem, it is a
particular style of statistical modeling, involving a host of theorems and
algorithms building on Bayes rule in a practical data analysis context.
Anyone may check out this website if they're curious for pointers into the
literature
There is no general consensus about the value of "Bayesian statistical
analysis", and many probabilists who are not among the "true believers",
agree with Christian's skeptical attitude.
Personally, I used to be more or less an adherent to one of the sects of the
Bayesian religions -- the Maximum Entropy Principle, which states that, in
many circumstances, the principle of entropy maximization should be used to
set Bayesian priors.
http://omega.albany.edu:8008/maxent.html
I still like Bayesian probability theory and I still like Maxent, but I
don't see them as quite the cure-all that their strongest adherents do.
While Eliezer's statements about BPT are strong, they are no stronger than
the ones made by some of the the MaxEnt advocates, who include plenty of
well-known scientists at prestigious institutions doing valuable practical
work.
What is good about the Bayesian approach to modeling is that it generally
requires fewer ad hoc up-front assumptions than the main alternative, which
is parametric statistics.
What is bad about it, is that it involves assuming priors, and while MaxEnt
is a good heuristic for setting priors, it's not perfect.
Autoclass is a great machine learning system based on Bayesian methods.
http://ic.arc.nasa.gov/ic/projects/bayes-group/autoclass/
In a lot of cases, it outperforms other unsupervised learning methods such
as clustering. Of course, every machine learning method has its adherents
and its detractors.
I think that elementary probability theory, including Bayes' Theorem, is one
of the most powerful tools for understanding the world that we have created.
Bayes Theorem itself is just part of the probability theory framework, of
course. It is true that almost any phenomenon can be modeled in
probability-theoretic terms.
However, although prob. theory has nearly universal applicability, I think
there are some aspects of the world that are not *conveniently* or
*usefully* modeled in terms of it. I think that many aspects of the mind
fall into this category.
-- Ben G
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