Example. Common seeds can reduce paired variance [ftip-00G0]
Example. Common seeds can reduce paired variance [ftip-00G0]
If \(s_M(Z)=s_{M'}(Z')\) almost surely under a common-seed coupling, then \(\widehat \Delta _m=0\) for every sample even when independent sampling would have nonzero variance. This is a variance statement, not evidence that the two artifacts have equal behavior on a different law.