ONT Re: Information = Comprehension x Extension -- Discussion

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ICE.  Discussion Note 46

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Hugh,

I will try to dispell some of the mystification over Bayes' Rule.
I learned my stats from math, stats, computer science, and psych
departments.  In all of these courses, Bayes' Rule was a theorem,
in fact a fairly trivial corollary of the standard definition of
a conditional probability.  If you call somebody a Pythagorean
because they use a particular formula for computing distances,
then that makes me a Bayesian by dint of the fact that I use
Bayes' Rule for computing the appropriate probabilities in
all of the settings where it applies.  But as a Bayesian,
in that sense, it always sounds a little odd to me when
the popular press talks about "Bayesian probabilities",
because they do it in a way that is very analogous to
speaking of "Pythagorean distances" only when going
from Chicago to Detroit, but never when going from
Detroit to Chicago.

Now the type of situation in which Bayes' Rule applies is one
where you have previously staked out a universe of discourse
with D's and S's, and you already know a sufficient number
of the conditional probabilities of the form P(S|D) that
you really already know the conditional probabilities
of the form P(D|S), only you don't know that you know
it yet until you crank the formula.  But if all your
D's are "Demons" and all your S's are "Sins", and if
there is no meaningful correspondence between these
nominal Demons and any sorts of real Diseases, nor
any significant relationship between these nominal
Sins and any sorts of real Symptoms, then all the
Bayesing at the moon in the world is not going to
help you fix your theory or cure your patients.

The first order of business in inquiry, then, is concerned with
the question of how one goes about forming these initial concepts
and theories, the order of groundwork that one needs before one can
even begin collecting data toward the estimation of any probabilities.
This is a stage of procedure where probabilistic reasoning cannot help,
because it precedes the entrance of definable probabilities on the scene
in question.

Depending on whether one treats the dance of inquiry as a fox-trot (2-step)
or a waltz (3-step), one will either treat this inchoative phase of inquiry
as some kind of mystical divination or bolt out of the blue that is beyond
the purview of methodological reflection and critique to examine and hope
to rationalize, or execute it as a step with its own interpretive logic.
The tune that Peirce piped is one that we've heard leads to waltzing.

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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