From Osher Doctorow
Readers should follow my ongoing thread in sci.physics in Probability-
Statistics in Physics, in which I showed that for Statistical
Dependence Dep(A, B) of set/events A, B:
1) DEP(A, B) = DEP_Log (A, B) - DEP_Non-log (A, B)
where logistic dependence DEP_Log(A, B) is defined as:
2) DEP_Log (A, B) = P(B)(1 - P(A))
and the second term on the right hand side of (1) is defined as:
3) DEP_Non-log (A, B) = P' (A-->B) - P(A-->B)
Furthermore:
4) P' (A-->B) = P(A-->B) + P(B)(1 - P(A|B))
We can generalized "logistic dependence" to "type 2" by replacing P(A)
in (2) above by the expression P(B|A):
5) DEP_2 Log(A, B) = P(B)(1 - P(A|B))
and therefore we can write (4) as:
6) P' (A-->B) = P(A-->B) + DEP_2 Log(A, B)
Comparing (1) and (6), DEP_Log(A, B) is used in the basic equation for
DEP(A, B), while DEP_2 Log(A, B) is used in the basic equation for
P' (A-->B). The latter is more fundamentally "Probable Causal" than
the former.
As a rule of thumb, it appears that the more (Probably) Causal the
equation or scenario, the more Logistic Dependence shifts from P(A) to
P(A|B) or P(A-->B) type factors.
Osher Doctorow
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