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Does the Supplementary Information (starting on p. 4, for example) help? https://static-content.springer.com/esm/art%3A10.1038%2Fs41586-024-07566-y/MediaObject
by mcguire 2y ago
Does the Supplementary Information (starting on p. 4, for example) help?
https://static-content.springer.com/esm/art%3A10.1038%2Fs41586-024-07566-y/MediaObjects/41586_2024_7566_MOESM1_ESM.pdf 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?
- bjourne 2y agoMaybe. "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.