I really need to spend some time describing Bayesian reasoning. I have a mental image, arising from reading Yudkowsky: for a simple problem, with evident property B and hidden property A; two horizontal bars, one above the other; the upper one of length P(A), the other of length P(~A); each is split horizontally in two, with the P(X|B) part on the left and the P(X|~B) on the right, for X in {A, ~A}. Line up the B vs ~B boundaries of the two bars vertically, draw diagonal line joining the bars' left ends and likewise for the right ends; see where they meet. Is the diagramatic fact useful in visualising the correct inference ? I think it should be: if the two bars are subdivided in the same proportions horizontally, the two diagonal lines shall meet on the centre-line of the bars (i.e. under the B vs ~B position); any imbalance shall shift the meeting-point to one side or the other.
It may help to use, as example, the inquisitor's over-seer. The inquisitor asks the accused whether she is a witch: she denies it. The inquisitor infers that she is a witch, since a witch would be likely to deny it. The over-seer asks, then, what was the purpose of the question; and how its outcome can influence the inquisitor's conviction of the accused's guilt.
christiansand re-incarnation
Another example to toy with: while reporting on the Chinese government's legislation governing re-incarnation (I kid thee not), Newseek tells me:
… could the next Dalai Lama be American-born?
You'll have to ask him,says Harrison. If so, he'll likely be welcomed into a culture that has increasingly embraced reincarnation over the years. According to a 2005 Gallup poll, 20 percent of all U.S. adults believe in reincarnation. Recent surveys by the Barna Group, a Christian research nonprofit, have found that a quarter of U.S. Christians, including 10 percent of all born-again Christians, embrace it as their favored end-of-life view.
from which I rapidly conclude that re-incarnation is more widely believed in
among folk who identify as christians than among the general adult population,
in the USA; and the born-again
crowd, though less apt to believe
in re-incarnation than the general adult population, aren't all fully persuaded
by orthodox christianity.