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  "body": "\n## Summary\n\nA [[statistic|0Q5CG2NEQ8]] is sufficient for a parameter when it keeps all the information that the sample contains about that parameter.\nOnce its value is known, the rest of the data has a distribution free of the parameter, so it says nothing more about it.\nSufficiency allows data reduction without loss, and it underlies the [[Rao–Blackwell theorem|Y3TX4J41TP]] and the theory of optimal estimators.\nThe [[Fisher–Neyman factorization theorem|Z6MF9ZGCMW]] gives a practical test for it.\n\n## Explanations\n\n### L1 human\n\nToss a coin $10$ times to learn its chance of heads.\nOnly the number of heads matters, not the order in which heads and tails came.\nGiven that there were $4$ heads, every order of $4$ heads and $6$ tails is equally likely, whatever the coin.\nSo the number of heads is a sufficient statistic: it compresses the data without losing anything about the coin.\n",
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