At 00:32 20/01/2004 +0000, you wrote:
From Osher Doctorow Ph.D. mdoctorow@comcast.net
In reply to Guy Marson, who asked what if one is depressed over being paranoid, it's an interesting idea but doesn't usually occur in that way (that is to say, being depressed over being paranoid) because it would require the paranoid person to be by definition angry at himself/ herself predominately in those circumstances.
Hi Osher, it was not me, I only contributed with a .par.. Am I paranoid? Maybe.. when I see my incoming mails: 80% Viagra and so on. My ´deformation´ (not a rare event) is still ok and not coming from a depression :-)))
A Paranoid person is predominately angry at others. It is theoretically possible, I do admit, for one to be exactly at the borderline of being equally angry at others and oneself, perhaps occasionally - for example, if one does poorly in an exam or a course, one could "kick oneself" as well as the "course" or (God forbid) the teacher. I suspect that in such a case one wouldn't be likely to make a vendetta against the teacher since one would realize one's own part in the poor performance in the course.
Regarding Deformation, I proved yesterday on sci.stat.math that:
1) P(A-->B) - P(B-->A) = P(B) - P(A) < = P(B/A) - P(A/B)
put this into a .frm,that makes me happy and I put it into the evolver..
if and only if A and B are statistically positive quadrant dependent, that is to say P(AB) > = P(A) times P(B). Let me translate this into English (those who want to know the technicalities I'll briefly discuss at the end). Inequality (1) says the the Rare Event difference in the probable influence of A on B and the probable influence of B on A reduces to the probability of B minus the probability of A and this in turn is less than or equal to the Fairly Frequent Event Conditional (Bayesian) probability of B given A minus the Conditional probability of A given B provided that A and B probably increase together rather than being unrelated or going in opposite directions.
This in turn describes an "avalanch" in probable influence somewhat similar to the way in which Rasputin's influence over Tsar Nicholas II and his wife Alexandra in Russia resulted largely in their unpopularity and ultimately largely in the Russian (Bolshevik) Revolution. The discrepancy in Rare Event probable influence, when it increases much, triggers a discrepancy in Fairly Frequent Event analogs or "given" type probabilities. They aren't pure analogs because "given" isn't the same idea as influence, but they're the closest that Conditional Probability comes to formulating probable influence.
For those interested in the math, P(B/A) = P(AB)/P(A) for P(A) not 0, and P(A-->B) = 1 + P(AB) - P(A). To prove the inequality very fast and easily, notice that algebraically P(B/A) - P(A/B) = [P(B) - P(A)] times P(AB)/(P(A)P(B))!
make an .frm for fractint of this stuff ..
Osher Doctorow
cheers, Guy