yy2bggggs
Master Poster
- Joined
- Oct 22, 2007
- Messages
- 2,435
B=0, C=0.325. You are presumably working with a fair coin that has heads on one side, right? (And may or may not have heads on both?)Ok.
H = The coin is two headed
E = 2 heads in a row
[P(H) =.5 <- this is a probability, not a premise]
...
The thing here is that I can't figure out a value for Pr(~E/H) and Pr(~E/~H). ~E means I don't get two heads in a row. But not getting two heads in a row doesn't mean I got a tails. Maybe I got 3 heads in a row,
The thing is, E is the result of some test. E' is also the result of the same kind of test--it is some actual result, with a value distinct from E. E' doesn't mean lack of E, but rather, presence of something not E; E means the test went one way--E' means it didn't go that way.
Furthermore, as another rule, all of your tests must be independent. For the same reason you can't just flip a coin twice, rewind the videotape, watch it get flipped twice again, and perform two inferences, you can't flip it three times, see what it got the first and second time, and see what it got the second and third time, and get two results. Two results means not less than 4 flips.
And finally, you must apply every result you get, or at least sample them randomly--you certainly cannot pick and choose your results (this would skew them). So if you flip the coin four times, you should apply two inferences (note that P(H|E')=P(H)P(E'|H)/P(E'); that is, it works perfectly fine when E is negated).
This case, mind you, is one where you pretty much know the exact values, except for the value of P(H). In this regard, figuring out these "atoms" is merely an exercise. The point of the atoms is to allow you to see deeper relationships between the big terms you're playing with, and allow you to see how certain changes in an estimate affects the fundamental sections of your universe, so that you know exactly how to estimate things fairly (which is still nothing but a guess, but a full understanding is necessary to keep you honest with yourself).