Estimation risk occurs in the almost universal situation where parameters of importance for decision making are not known with certainty. Bayes' criterion is the procedure consistent with expected utility maximization in the presence of estimation risk. Three interrelated problems in the presence of estimation risk are analyzed: (i) the choice of the utility-maximizing decision rule in a mean-variance framework, (ii) the calculation of certainty equivalent returns, and (iii) the valuation of additional sample information.