User:Woozle/positions/9-11/Bayesian

About
This is a hack-attempt at a Bayesian analysis (see lwwiki:Conservation of expected evidence) of the hypothesis "high-ranking US officials were involved in the 9/11 attacks on at least a LIHOP (Let It Happen On Purpose) level", which I will refer to as Hypothesis H.

I'm not sure I'm intellectually equal to the task of figuring out my "priors". I understand the concept somewhat when it comes to things like flipping coins which might or might not be rigged in a certain way, but where do you start when dealing with unquantified possibilities involving non-quantitative entities such as people and motives?

The questions we're trying to answer, if I understand rightly, are:
 * A - =P(H) - What is the likelihood of H being true in the absence of evidence E?
 * B - P(E|H) - What is the likelihood that evidence E would occur if H were true?
 * C. - P(~E|H) - What is the likelihood that evidence E would not occur if H were true?
 * D. What does evidence E therefore tell us about the odds against H being true?

(P(A|B) means the probability of A given B)

Maybe I'm misunderstanding here, because it would seem more relevant to evaluate P(E|~H) -- the odds that you'd see the same evidence even if the hypothesis was wrong -- than to evaluate P(~E|H), because P(~E|H) will always be 1.0-P(E|H) so you're not adding any new information doing it that way.

I'm going to assume I'm right about that, and replace C with:
 * C. - P(E|~H) - What is the likelihood that evidence E would occur even if H were false?

At this point, however, I get lost trying to figure out what the final calculations should be, and I've already spent most of today arguing 9/11 stuff when I should have been working, so abandoning this for now.

Eventually we're going to need to list the pieces of evidence and evaluate them; towards that end, here are the relevant bits of evidence I've been able to think of:

Evidence for

 * 1. Cheney in the PEOC: "have I given you any reason to think [that the orders don't still stand?]" as AA11 was homing in on the Pentagon
 * 2. Bush remaining in a well-known not-very-secure position for, what, half an hour?, under the landing path at a major airport, when the country is supposedly under attack by hijacked airplanes
 * 3. The military's behavior before (scheduling so many similar simulation exercises on the day of the event), during (orders lost, planes misdirected), and after (nobody was punished, and some were promoted) speaks of high-level involvement.
 * 4. The fact that nobody in the administration seemed to be at all upset about how quickly the evidence was hauled off, or any of the other problems with the investigation
 * 5. The fact that Bush had to be wrestled into having an investigation at all, a year after the event.
 * 6. The fact that ongoing investigations into people who later became the 9/11 hijackers were hindered or actively blocked by "orders from the top"

Evidence against

 * 1. Bush is a twit; unlikely that he could plan anything complicated and not screw up. Either someone else was planning it and he just helped, or he was "outside the loop"; in any case, you're "needlessly multiplying entities" (which makes William of Occam cry). One more person to be either in on the conspiracy or else carefully maneuvered around it. On the other hand, Hypothesis H doesn't require Bush himself to be involved... so this is a weak argument against, although valid.
 * 2. What human would do such a thing? Well, Bushco aren't human, they're neocons... but still, it's a heckuvva nallegation...
 * 3. Why would the president of the US want to see his own country attacked? Well, political gain... but still!