Admissible estimators of binomial probability and the inverse Bayes rule map (Q921762)

Let \(X\) be a binomial random variable with parameters n and \(\theta\), where \(\theta\) is an unknown binomial probability, and consider the Bayes estimation of \(\theta\) relative to a prior distribution \(\mu\). The authors obtain explicit formulae for the moments of the prior distribution through the values of the Bayes estimator, and use these to derive a new admissibility criterion.