Bayes estimator

Summary

A Bayes estimator is an estimator that minimizes the Bayes risk, the risk averaged over a prior distribution on the parameter. In practice it minimizes, for each observed data set, the expected loss under the posterior distribution. Under squared error loss it is the posterior mean. Bayes estimators link Bayesian inference with frequentist decision theory, since they are central in the study of admissible and minimax rules.