I tend to informally use ε for shorthand for “anything with a small enough probability that competing hypotheses like ‘I have gone insane’ dominate”. Which I freely admit is somewhat sloppy.
Because if you ask this person what kind of evidence would change their estimate from “epsilon” to, say, 5%, they would be hard pressed to come up with anything sensible.
...that’s kind of the point. In informal use, I tend to use ε for shorthand for cases where there aren’t any sensible ways to update to, say, 5% probability of the thing happening.
Saying zero would draw out pedants saying, “but zero isn’t a probability, are you really infinitely certain, etc. etc.” Although personally I would just say zero and ignore the pedants.
Ignoring pedants is correct, but I find value in the acknowledgement and reminder that it’s not ACTUALLY zero, but just small enough for me not to estimate it or think much about it in normal circumstances.
I tend to informally use ε for shorthand for “anything with a small enough probability that competing hypotheses like ‘I have gone insane’ dominate”. Which I freely admit is somewhat sloppy.
...that’s kind of the point. In informal use, I tend to use ε for shorthand for cases where there aren’t any sensible ways to update to, say, 5% probability of the thing happening.
Well, why don’t you use zero instead, what is the difference, instrumentally?
Because remembering the structure of things is instrumentally useful.
Saying zero would draw out pedants saying, “but zero isn’t a probability, are you really infinitely certain, etc. etc.” Although personally I would just say zero and ignore the pedants.
Ignoring pedants is correct, but I find value in the acknowledgement and reminder that it’s not ACTUALLY zero, but just small enough for me not to estimate it or think much about it in normal circumstances.