On Tue, Nov 19, 2002 at 09:54:13AM -0600, Bob Apthorpe wrote:
> > What does "joint and conditional frequency analysis" mean?
> 
> First, start with Larry Gonick's fantastic "The Cartoon Guide To Statistics":
> http://www.powells.com/cgi-bin/biblio?inkey=7-0062731025-0
> 
> Being neither a mathematician nor a statistician, sounds like joint
> frequency analysis is how you derive P(A and B), and conditional frequency
> analysis is how you generate P(A given B) (generally written P(A|B)),
> where A and B are two events (in this case, the occurrence of words A and
> B, respectively.) Bayes' Theorem boils down to P(A|B) = P(A and B)/P(B), which 
> is intuitive if you draw the big Venn diagram.

Very good analysis!  My probability professor would be proud of that
explanation.  The only gripe I have is with your definition of Bayes's
theorem.

The really controversial point about Bayes's work was his work after the
derivation you suggested above (strictly speaking, P(A|B)=P(A&B)/P(B) is
just the formula for conditional density - ie, A given B).

Bayes went on to model how confident you could be of the decision
resulting from the probability calculations.  AI people aparantly love
the idea - mathematical philosophers hate it because it's a subjective
measurement.

In this case it doesn't really matter since we have a rigorous
definition for the confidence (determined by the spam/non-spam corpus).

-- 
Ross Vandegrift
[EMAIL PROTECTED]

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