Oh, in that case I’d take the “no” side at 5:1 odds or lower. (I’m metauncertain enough that I wouldn’t dare make bets in either direction close enough to my break-even point.)
Hmm. Actually, it’s because I haven’t bothered to collect all the information I could, and so my bid-ask spread serves as a confidence interval. If it were too small, then I’d actually find it probable that someone else could do the research I haven’t, figure out that the true value is on one side or the other of my interval, and exploit me.
If it were too small, then I’d actually find it probable that someone else could do the research I haven’t, figure out that the true value is on one side or the other of my interval, and exploit me.
This makes sense. So the interval at which you were willing to bet would increase given higher stakes (as that would give someone more incentive to do the research)?
What I’m trying to understand is what confidence interval means in a Bayesian context, a ‘credible interval’ seems to be the analogous concept but even after reading the article I’m still quite confused as to what a credible interval is in the context of subjective probability. I’ve seen also seen people here refer to the ‘stability’ of their beliefs- a concept which seems to function similarly. It definitely feels like it would be useful tool- it just don’t quite get what it would mean as a way of describing beliefs instead of repeatable trials.
And if we can talk about credible intervals for beliefs… isn’t that really relevant information for predictions? Shouldn’t we give intervals in addition to p values? I’m not sure it makes sense to assume normal distributions for casually calculated probabilities on one-off events. This is especially the case since humans are really, really bad at distinguishing between probabilities at extremely high and low levels.
One way to think about the bid-ask spread, is that while orthonormal’s current probability is 10%, he’d consider someone offering to bet him actual money on one side or the other to be sufficient evidence to adjust his belief significantly in that direction.
I was thinking along the lines of Skatche’s reasoning above. 10% is my break-even point; if you were willing to go against me at 19:1, I’d take it.
I didn’t make myself clear—it’s the other side of the bet I want!
Oh, in that case I’d take the “no” side at 5:1 odds or lower. (I’m metauncertain enough that I wouldn’t dare make bets in either direction close enough to my break-even point.)
At those odds a bet is almost but not quite worth it I think!
OK, so it seems our estimates are within the same bid-ask spread.
EDIT: Or rather, our bid-ask spreads intersect.
The meta-uncertain excuse doesn’t make a lot of sense to me- it’s enough that you want enough expected gain to justify the transaction cost.
Or is there some kind of rigorous notion of meta-uncertainty you’re appealing to?
Hmm. Actually, it’s because I haven’t bothered to collect all the information I could, and so my bid-ask spread serves as a confidence interval. If it were too small, then I’d actually find it probable that someone else could do the research I haven’t, figure out that the true value is on one side or the other of my interval, and exploit me.
This makes sense. So the interval at which you were willing to bet would increase given higher stakes (as that would give someone more incentive to do the research)?
What I’m trying to understand is what confidence interval means in a Bayesian context, a ‘credible interval’ seems to be the analogous concept but even after reading the article I’m still quite confused as to what a credible interval is in the context of subjective probability. I’ve seen also seen people here refer to the ‘stability’ of their beliefs- a concept which seems to function similarly. It definitely feels like it would be useful tool- it just don’t quite get what it would mean as a way of describing beliefs instead of repeatable trials.
And if we can talk about credible intervals for beliefs… isn’t that really relevant information for predictions? Shouldn’t we give intervals in addition to p values? I’m not sure it makes sense to assume normal distributions for casually calculated probabilities on one-off events. This is especially the case since humans are really, really bad at distinguishing between probabilities at extremely high and low levels.
One way to think about the bid-ask spread, is that while orthonormal’s current probability is 10%, he’d consider someone offering to bet him actual money on one side or the other to be sufficient evidence to adjust his belief significantly in that direction.