Re: collective intelligence - bayes theorem help

["Jonathan Tran" <jonnytran@gmail.com>]

> Right, and what if in my example, state  doesn't impact the probability at
> all.  If belonging to Philly lambda is the key determining factor then
> taking state into account only throws us out of whack.

Are you saying you flat out _know_ that state doesn't impact the
probability?  ... as in, you're making that simplification?  Or are
you asking, "What if the state doesn't really matter?  How will that
affect the calculation?"

Because I was going to say that, as Gabriel pointed out, state and
group are not necessarily independent.  ...in which case, your
assumption is incorrect.

P(B and C) = P(B)*P(C) if B and C are independent.
But P(B and C) is not generally equal to P(B)*P(C)

(This is true of any B, C, not just yours.)

Similarly,
P(A|B and C) is not generally equal to P(A|B)*P(A|C).

If you want to put attributes together like that, you literally have
to go through your dataset and recompute the probability of following
a person given each combination of attributes, since (I'm guessing)
the attributes are not independent.  Someone might be more likely to
be in Philly Lambda if they live in NJ, as opposed to FL, and so P(B
and C) will be different than P(B)*P(C).  (But then again, maybe you
don't care about people living outside of driving range from Philly
Lambda, so as a simplification, you might say they're independent.)