Really? I was approaching this as a normally distributed set, which might have been wrong.
I'm actually familiar with Bayes's theorem, but this assumes three values: a priori odds, a posteriori odds, and a likelihood ratio. We can calculate the likelihood ratio, but these are the a posteriori odds in my example. What Bayes's theorem is most useful for is to calculate the probability of evidence being circumstantial when other data is present. However, in most experiments, no other data will be present (otherwise your experiment is probably wrong). Also, no a priori odds are present.
It might be possible to express how valuable your evidence is by calculating the likelihood ratio, taking the blank experiment as being the a priori odds and the actual test as the a posteriori odds, but it's fairly hard to express a minimum value which would count as actual proof. Aside from that, increasing the number of experiments will increase the significance, but will not increase the likelihood ratio resulting from a bayesian formula, which I personally feel does not properly show the value of attained results.
For this reason, I think it's better to approach experiments like these as being normally distributed sets of data, but this is of course very much dependent on the experiment being run.
What you have structured in that article is not a conditional probability; therefore, it is not a hypothetical set up, for a hypothesis is a conditional statistical set up. You are correct in that it assumes an an priori value; however, all scientific hypothesis have to have one. It seems that you used the very trivial Kolmogorov axioms where P(Ω) = 1 where the sum of the measurements for the subspace add up to P(E); however, this tells you nothing, scientifically. What it seems like you have done is that you took the basic axioms of what a probability is - P(E), where you have then combined it with enumerable instances, added up the sum, and came up with a value that doesn't give you an a priori value. Bayes Theorem basically is P(A) (the prior belief that x will happen) relative to P(B) (the inverse of x not happening). What you have in that article basically just says that if we add up the measurements of a subset, we get a probability; however, it does not provide statistical criteria if a hypothesis holds true. Your approach to experimental set up doesn't given one a criteria on which it is disproven or proven. Since we have no a priori value to compare the a posteri value to, I don't see what increasing experiments will do. P(E)=1 just simply says that something is a total probability or that something is a non-zero probability. It has no hypothetical relevance.
