I disagree. It can be rational to shift subjective probabilities by many orders of magnitude in response to very little new information.
What your example looks like is a nearly uniform prior over a very large space- nothing’s wrong when we quickly update to believe that yesterday’s lottery numbers are 04-15-21-31-36.
But the point where you need to halt, melt, and catch fire is if your prior assigns the vast majority of the probability mass to a small compact region, and then the evidence comes along and lands outside that region. That’s the equivalent of starting out 99.99% confident that you know tomorrow’s lottery numbers will begin with 01-02-03, and being proven wrong.
Yes, you’re right, I wasn’t thinking clearly, thanks for catching me. I think there’s something to what I was trying to say, but I need to think about it through more carefully. I find the explanation that you give in your other comment convincing (that the point of the graphs is to clearly illustrate the principle).
What your example looks like is a nearly uniform prior over a very large space- nothing’s wrong when we quickly update to believe that yesterday’s lottery numbers are 04-15-21-31-36.
But the point where you need to halt, melt, and catch fire is if your prior assigns the vast majority of the probability mass to a small compact region, and then the evidence comes along and lands outside that region. That’s the equivalent of starting out 99.99% confident that you know tomorrow’s lottery numbers will begin with 01-02-03, and being proven wrong.
Yes, you’re right, I wasn’t thinking clearly, thanks for catching me. I think there’s something to what I was trying to say, but I need to think about it through more carefully. I find the explanation that you give in your other comment convincing (that the point of the graphs is to clearly illustrate the principle).