Comment by mcguire
2 years ago
Does the Supplementary Information (starting on p. 4, for example) help?
https://static-content.springer.com/esm/art%3A10.1038%2Fs415...
In your counterexample, can you quantify "as long as the samples are large enough"? How many samples do you need to keep the s.d. from shrinking?
Maybe. "Overall, this only shows us how far on average we go from the original distribution, but the process can only ’terminate’ if the estimated variance at a certain generation becomes small enough, i.e. we effectively turn into a delta function." Iiuc, variance is modeled as a random walk that will sooner or later reach on zero. I'm not sure I buy that because the variance "walks" orders of magnitudes slower than the mean and is much more robust for large sample sizes.