The classic answer is that your confidence intervals are liable to occasionally tell you that mass is a negative number, when a large error occurs. Is this interval allowing only negative masses, 90% likely to be correct? No, even if you used an experimental method that a priori was 90% likely to yield an interval covering the correct answer. In other words, using the confidence interval as the posterior probability and plugging it into the expected-utility decision function doesn’t make sense. Frequentists think that ignoring this problem means it goes away.
I already gave Cyan that classic answer, complete with a link to Jaynes, in this very comment thread. :-) But it doesn’t settle the problem completely for me. It feels like finger-pointing. Yes, frequentists have lower quality answers; but why isn’t the average calibration of a billion Bayesians in any way related to that 90% number that they all use?
The classic answer is that your confidence intervals are liable to occasionally tell you that mass is a negative number, when a large error occurs. Is this interval allowing only negative masses, 90% likely to be correct? No, even if you used an experimental method that a priori was 90% likely to yield an interval covering the correct answer. In other words, using the confidence interval as the posterior probability and plugging it into the expected-utility decision function doesn’t make sense. Frequentists think that ignoring this problem means it goes away.
They don’t.
I don’t mean the negative-answer problem. I mean “the confidence interval simply is not the posterior probability full stop” problem.
Well, sure. But whither calibration?
I already gave Cyan that classic answer, complete with a link to Jaynes, in this very comment thread. :-) But it doesn’t settle the problem completely for me. It feels like finger-pointing. Yes, frequentists have lower quality answers; but why isn’t the average calibration of a billion Bayesians in any way related to that 90% number that they all use?