I don’t know what this means. On the basis of what would you decide what’s “reasonable” and what’s not?
There is a time-honored and quite popular technique called pulling numbers out of your ass. Calling it “intuition” doesn’t make the numbers smell any better.
See “If It’s Worth Doing, It’s Worth Doing With Made-Up Statistics” on Slate Star Codex, though I agree that a human’s intuition for probabilities well below 1e-9 is likely to be very unreliable (except for propositions in a reference class containing billions of very similar propositions, such as “John Doe will win the lottery this week and Jane Roe will win the lottery next week”).
The only thing that matters is making successful predictions. How they smell doesn’t.
To know at whether a method makes successful predictions you calibrate the method against other data. That then gives you an idea about how accurate your predictions happen to be.
Depending on the purpose for which you need the numbers different amounts of accuracy is good enough.
I’m not making some Pascal mugging argument that people are supposed to care more about Zeus where I need to know the difference between 10^{-15} and 10^{-16}. I made an argument about how many orders of magnitude my beliefs should be swayed.
My current belief in the probability of Zeus is uncertain enough that I have no idea if it changed by orders of magnitude, and I am very surprised that you seem to think the probability is in a narrow enough range that claiming to have increased it by order of magnitude becomes meaningful.
No, I can’t. Heuristics are a kind of algorithms that provide not optimal but adequate results. “Adequate” here means “sufficient for a particular real-life purpose”.
I don’t see how proclaiming that the probability of Zeus existing is 10^-12 is a heuristic.
I don’t know what this means. On the basis of what would you decide what’s “reasonable” and what’s not?
There is a time-honored and quite popular technique called pulling numbers out of your ass. Calling it “intuition” doesn’t make the numbers smell any better.
See “If It’s Worth Doing, It’s Worth Doing With Made-Up Statistics” on Slate Star Codex, though I agree that a human’s intuition for probabilities well below 1e-9 is likely to be very unreliable (except for propositions in a reference class containing billions of very similar propositions, such as “John Doe will win the lottery this week and Jane Roe will win the lottery next week”).
The only thing that matters is making successful predictions. How they smell doesn’t. To know at whether a method makes successful predictions you calibrate the method against other data. That then gives you an idea about how accurate your predictions happen to be.
Depending on the purpose for which you need the numbers different amounts of accuracy is good enough. I’m not making some Pascal mugging argument that people are supposed to care more about Zeus where I need to know the difference between 10^{-15} and 10^{-16}. I made an argument about how many orders of magnitude my beliefs should be swayed.
My current belief in the probability of Zeus is uncertain enough that I have no idea if it changed by orders of magnitude, and I am very surprised that you seem to think the probability is in a narrow enough range that claiming to have increased it by order of magnitude becomes meaningful.
You can compute the likelihood ratio without knowing the absolute probability.
Being surprised is generally a sign that it’s useful to update a belief.
I would add that given my model of you it doesn’t surprise me that this surprises you.
You can call it heuristics, if you want to...
No, I can’t. Heuristics are a kind of algorithms that provide not optimal but adequate results. “Adequate” here means “sufficient for a particular real-life purpose”.
I don’t see how proclaiming that the probability of Zeus existing is 10^-12 is a heuristic.
Intuition (or educated guesses like the ones referred to here), fall under the umbrella of heuristics.
In what way are you arguing that the number I gave for the existence of Zeus is insufficient for a particular real-life purpose?