alt Hacker News> Second, besides noise (bars are Wilson 95% confidence intervals, very conservative for run-to-run noise), there is little difference down to 4-bit; only the 2-bit scores a bit lower.
Confidence intervals have nothing to do with run-to-run variation. They have little to do with anything people usually ascribe to them (https://link.springer.com/article/10.3758/s13423-015-0947-8 ), but even less with run-to-run variation (https://link.springer.com/article/10.1007/s10654-016-0149-3 misconception 22).
Replies
> The key confusion underlying the FCF is the confusion of what is known before observing the data — that the CI, whatever it will be, has a fixed chance of containing the true value — with what is known after observing the data. Frequentist CI theory says nothing at all about the probability that a particular, observed confidence interval contains the true value; it is either 0 (if the interval does not contain the parameter) or 1 (if the interval does contain the true value).
They're really reaching here. There's a 95% chance it's 1 and 5% it's 0, and we don't know which, so it's 0.95. Like saying the probability your uncle died of a shark attack is either 0 or 1. But in reality I don't know anything about your uncle so it's the average probability that someone picked randomly died of a shark attack, until I know it about your uncle.
Task success is not enough; reliability and cost matter.
Yah, prediction interval instead, right? (I'm still learning statistics)
Saying there's a confidence interval for run-to-run makes no sense, from the way I understand it, because each run could have a result that's all over the place.
Mind blown. The more I read about statistics, the less I know.
Thank you for these, coz I learned a lot! Great that they are open access.
the 2nd derivate of shannon covariance of noise begs to differ
Point taken, but there is a much more fundamental issue with it - and precisely why I wrote "very conservative".
It is a different problem if we pick two sets from the same data distribution, A and B, and first we have a score on A, then on B. Here we re-run on precisely the same set of Terminal Bench 2.1 problems. It may be that results are so random between runs that each single task has the same probability in a Bernoulli distribution. But more likely, many problems are easy (i.e. each run will solve them consistently), many are too hard (i.e. no run is going to solve them) and only a fraction is somehow in between.
Maybe there is some good trick to find a proper distribution, but to my knowledge, we would need to run it at least two times on TB2.1 to get any more educated estimates. That said, I am open to new ideas.
That said, I consider frequentist probability a dirty trick, and that Bayesian is the proper way of doing things (vide David J.C. MacKay" Information Theory, Inference, and Learning Algorithms" and Cam Davidson-Pilon "Probabilistic Programming & Bayesian Methods for Hackers" https://www.inference.org.uk/itprnn/book.pdf, https://dataorigami.net/Probabilistic-Programming-and-Bayesi...).