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  "body": "\n## Summary\n\nA Bayes estimator is an estimator that minimizes the [[Bayes risk|VEBDNCJJTN]], the risk averaged over a prior distribution on the parameter.\nIn practice it minimizes, for each observed data set, the expected loss under the [[posterior distribution|0KJ7ZS8AJA]].\nUnder squared error loss it is the posterior mean.\nBayes estimators link [[Bayesian inference|0JWRJX2RMP]] with frequentist decision theory, since they are central in the study of admissible and minimax rules.\n\n## Explanations\n\n### L1 human\n\nBefore seeing the data, a Bayesian describes beliefs about the unknown quantity by a prior distribution.\nAfter seeing the data, the beliefs are updated to a posterior distribution.\nThe Bayes estimator is the single number that is best on average according to these updated beliefs.\nFor a coin with a uniform prior on its heads probability, $x$ heads in $n$ tosses give the Bayes estimate $(x + 1)/(n + 2)$ under squared error.\n",
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