I’m used to seeing normal (or log-normal) distributions fit to subjective confidence intervals—because the confidence intervals are being used to do some subjective probabilistic analysis. I assumed that was what you were doing, given that you were using the actual attained value x, and not just which of the three possibilities A:(x < left), B:(left < x < right), and C:(right < x) occurred.
Hmmm… you seem to have evaded the theorem about the only strictly proper local scoring rule being the logarithmic score, by only seeking to find the confidence interval, but using more information than just the region (A, B, or C) the outcome belongs to.
It would help to see a proof of the claim; do you have a reference or a link to a URL giving the proof?
Oh, a quick thing thats not a proof that may convince you it is true:
It works exactly the same way as saying that measuring the distance between reported value and true value incentivizes honest reporting of your median. (The point you think it the true value is above with probability 50%)
I’m used to seeing normal (or log-normal) distributions fit to subjective confidence intervals—because the confidence intervals are being used to do some subjective probabilistic analysis. I assumed that was what you were doing, given that you were using the actual attained value x, and not just which of the three possibilities A:(x < left), B:(left < x < right), and C:(right < x) occurred.
Hmmm… you seem to have evaded the theorem about the only strictly proper local scoring rule being the logarithmic score, by only seeking to find the confidence interval, but using more information than just the region (A, B, or C) the outcome belongs to.
It would help to see a proof of the claim; do you have a reference or a link to a URL giving the proof?
I dont have a reference. gjm’s comment gives a quick sketch.
Oh, a quick thing thats not a proof that may convince you it is true:
It works exactly the same way as saying that measuring the distance between reported value and true value incentivizes honest reporting of your median. (The point you think it the true value is above with probability 50%)