So, suppose I know the stopping criterion and the number of button presses that it took to stop the sequence, but I wasn’t given the actual sequence.
It seems to me like I can use the two of those to recreate the sequence, for a broad class of stopping criteria. “If it took 100 presses, then clearly it must be 70 1s and 30 0s, because if it had been 71 1s and 29 0s he would have stopped then and there would be only 99 presses, but he wouldn’t have stopped at 69 1s and 30 0s.” I don’t think I have any additional info.
Should you update your belief on the hidden double after hearing of my deception? Obviously you should.
Update it to what? Assuming that the data is not tampered with, just that your stopping criterion was pointed at a particular outcome, it seems like that unless the double is actually very close to 0.42 then you are very unlikely to ever stop!* It looks like the different stopping criteria impose conditions on the order of the dataset, but the order is independent of the process that generates whether each bit is a 1 or a 0, and thus should be independent of my estimate of the hidden double.
* If you imagine multiple researchers, each of which get different sequences, and I only hear from some of the researchers- then, yes, it seems like selection bias is a problem. But the specific scenario under consideration is two researchers with identical experimental results drawing different inferences from those results, which is different from two researchers with differing experimental setups having different distributions of possible results.
So, suppose I know the stopping criterion and the number of button presses that it took to stop the sequence, but I wasn’t given the actual sequence.
It seems to me like I can use the two of those to recreate the sequence, for a broad class of stopping criteria. “If it took 100 presses, then clearly it must be 70 1s and 30 0s, because if it had been 71 1s and 29 0s he would have stopped then and there would be only 99 presses, but he wouldn’t have stopped at 69 1s and 30 0s.” I don’t think I have any additional info.
Update it to what? Assuming that the data is not tampered with, just that your stopping criterion was pointed at a particular outcome, it seems like that unless the double is actually very close to 0.42 then you are very unlikely to ever stop!* It looks like the different stopping criteria impose conditions on the order of the dataset, but the order is independent of the process that generates whether each bit is a 1 or a 0, and thus should be independent of my estimate of the hidden double.
* If you imagine multiple researchers, each of which get different sequences, and I only hear from some of the researchers- then, yes, it seems like selection bias is a problem. But the specific scenario under consideration is two researchers with identical experimental results drawing different inferences from those results, which is different from two researchers with differing experimental setups having different distributions of possible results.