From: Christian L. (n95lundc@hotmail.com)
Date: Fri Aug 30 2002 - 08:56:08 MDT
Ben wrote:
>
>Eliezer wrote:
> > 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...
Yes, it was a curious blind spot on my part. I will check out the links in
your mail. I sometimes come across people who have made sweeping
generalizations about mathematics without really knowing any math at all, so
I guess that Eliezer's poetic tribute triggered some kind of memetic immune
response.
>
>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.
Bayes' Theorem supposes that we have a universal set U which is subdivided
into disjunct subsets H_1, ..., H_n. Then, given an event A,
the probability of H_i when A has happened, P(H_i | A), can be calculated as
P(H_i | A) = P(H_i)*P(A | H_i) / (\sum_j P(H_j)*P(A | H_j))
What I have heard, the controversy that sometimes arises out of the use of
this theorem is due to the fact that the probabilities P(H_j) are often very
difficult to calculate, so you can distort your data by setting the
probabilities P(H_j) in a sloppy fashion.
Am I correct in saying that the different Bayesian philosophies are
concerned with methods of setting these probabilities (are these the
"priors" you discuss?) in a careful way? Or is this too simplistic?
Maybe we are getting off topic here...
/Christian
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