Yes, thats the concept to which I am refering. The concept comes from measure theory. If you’re familiar with I’m not sure why you’re confused about probability 0 events.
I think her confusion comes from the fact that if your prior probability that an event happened is 0, no amount of evidence will convince you that it did happen. Suppose your prior probability that some random variable X is equal to 1 is P(X=1)=0. Now suppose you find out that actually, X=1. Then using Baye’s rule:
P(X=1|X=1) = P(X=1|X=1)*P(X=1) / denominator
I’ll leave the denominator out because the numerator is 0 (the denominator won’t be 0), so P(X=1|X=1)=0, which makes no sense.
I don’t claim the calculation I did above is correct—I realize conditional probabilities a fraught with difficulties, and I probably violated some rule I don’t know about or have forgotten from my measure theory class. However, this does give you intuition for why lucidfox or perhaps someone else would be confused despite having knowledge of measure theory (if this is in fact why it was confusing to him/her).
No finite amount of evidence will convince you. I can be convinced of infinitely unlikely things by an infinite amount of evidence just fine.
And if we’re talking about a situation (like real life!) where you can’t expect to receive an infinite amount of evidence, then we shouldn’t be using probabilities of 0 or 1, either.
I think her confusion comes from the fact that if your prior probability that an event happened is 0, no amount of evidence will convince you that it did happen. Suppose your prior probability that some random variable X is equal to 1 is P(X=1)=0. Now suppose you find out that actually, X=1. Then using Baye’s rule:
P(X=1|X=1) = P(X=1|X=1)*P(X=1) / denominator
I’ll leave the denominator out because the numerator is 0 (the denominator won’t be 0), so P(X=1|X=1)=0, which makes no sense.
I don’t claim the calculation I did above is correct—I realize conditional probabilities a fraught with difficulties, and I probably violated some rule I don’t know about or have forgotten from my measure theory class. However, this does give you intuition for why lucidfox or perhaps someone else would be confused despite having knowledge of measure theory (if this is in fact why it was confusing to him/her).
No finite amount of evidence will convince you. I can be convinced of infinitely unlikely things by an infinite amount of evidence just fine.
And if we’re talking about a situation (like real life!) where you can’t expect to receive an infinite amount of evidence, then we shouldn’t be using probabilities of 0 or 1, either.
Her confusion.