I see. so -
If P(H) = 1.0 - ϵ1
And P(E|H) = 0 + ϵ2
Then it equals “infinite confusion”.
Am i correct?
and also, when you use epsilons, does it mean you get out of the “dogma” of 100%? or you still can’t update down from it?
And what i did in my post may just be another example of why you don’t put an actual 1.0 in your prior, cause then even if you get evidence of the same strength in the other direction, that would demand that you divide zero by zero. right?
Using epsilons can in principle allow you to update. However, the situation seems slightly worse than jimrandomh describes. It looks like you need P(E|h), or the probability if H is false, in order to get a precise answer. Also, the missing info that jim mentioned is already enough in principle to let the final answer be any probability whatsoever.
If we use log odds (the framework in which we could literally start with “infinite certainty”) then the answer could be anywhere on the real number line. We have infinite (or at least unbounded) confusion until we make our assumptions more precise.