Jabba, if you guess at what a die will roll, roll the die, and get the number you guessed, you were "lucky". The more sides the die has, the more lucky your correct guess was (that is, the more unlikely it would be that the number you guessed in advance would come up).
But that's not the situation here. You didn't exist before the die was rolled. You are the number that happened to come up. Nobody guessed it before the roll. The number that came up does not correspond to any number anyone picked before it was rolled. It's not a coincidence, just an incident.
- Dave,
- I would say that prediction is not the only way that a specific improbable event gets set apart from its crowd. I'll try to expand upon that tomorrow.
- 100 students, taught by 5 different teachers, take the same exam. The null hypothesis is that when taking the test, there was no significant difference between the the knowledge of the 5 different populations.
- It turns out, however, that the top 7 scores were received by students of Ms Smith. These scores set Ms Smith's class apart from the other classes -- they suggest at least one of two alternative hypotheses: Ms Smith was the best teacher in this case and/or she had (for some reason) been assigned the best students.
- I suspect that I should hereby
slow down...
- My example involves something like prediction...
- For me, this is the key question -- what is the principle that sets me apart from the rest of you schmucks, for our purposes here? (Or really, what's the principle that sets us scmucks apart from the blank wall?)
- What's the principle that sets apart one event from a multitude of other similar events -- and, in our formula, allows the entered likelihood of the particular event to be the likelihood specific to it rather than the likelihood general to any example of those similar events?
- So far, I can't even express this question with any confidence of it being understood... If you think you know what I'm trying to ask, see if you can ask it better.
- Anyway, I think that I am justified in using 1/10
80! as P(me|A) instead of 1.00 -- and, the specific question is, "What sort of characteristic of "me" would it take to separate me from the masses, and to logically use 10
80! as P(me|A) in the Bayes formula?
- I'll be back.