Posted: Jan 08, 2015 5:30 pm
by Lowpro
Thommo wrote:
Lowpro wrote:I have a mostly similar position but one difference. If you do not have data for a position (and I mean data in a strict information stance) then you have NO POSSIBILITY. A probability can be inferred with a sample size of 1, it just will lack meaningful confidence (variation within a sample of 1 is enough). That's mathematics.


Could you elaborate on this? All the likelihood estimation techniques (and similar) I've ever seen have requirements on sample size, 1 is never enough - to say something has a probability of 0.5 ± 0.5 is to say you have no information at all - by definition probability is already in the range 0 ≤ p ≤ 1.


What MLE modelling techniques have you seen? Keep this is mind right now. Probability modeling only cares about variation; more than one measurement. A sample size of 1 would be one coin, two states: Heads or Tails. You can determine likelihood without ever flipping that coin once because you know it's variation, you just will have very little confidence in it (in the case of an unfair coin). That's the point of why probability modeling is easy; the confidence is what matters though.

Now if there's no possibility then we have NO information. Imagine we have a coin with two states, heads and tails, but it is unfair and will NEVER land heads up. You could write a probability of 0.5 for both, but landing heads up is NOT POSSIBLE and if you tested this you'll never have the necessary variation (it will always lands tails up).

The probability works, the possible does not. God has no information, no variation, thus is impossible. Even if we had some sufficient probability of God, it would be impossible.

Fun fact: N of 1 studies happen often and they're definitely modelable.