not just about the probability you think something is true, but an estimate of your confidence, in some quantitative way?
I don’t think these are actually different things.
The coin example is misleading. Your confidence in the next toss being heads is exactly the same as any other independent 50% bet. Your confidence that “this is a fair coin”, which could be approximated by, say, getting between 45-55 heads in the next 100 tosses, is a different bet and will give a different answer than 50%.
I don’t think these are actually different things.
The coin example is misleading. Your confidence in the next toss being heads is exactly the same as any other independent 50% bet. Your confidence that “this is a fair coin”, which could be approximated by, say, getting between 45-55 heads in the next 100 tosses, is a different bet and will give a different answer than 50%.