The problem of sequential estimation of the mean, subject to the loss defined as the sum of squared error loss and sampling costs, is considered within the Bayesian framework. It is shown that the sequential procedure, as proposed by Chow and Yu (1981) in classical non-Bayesian sequential estimation, is, in fact, asymptotically Bayes for a large class of prior distributions. The proposed procedure, without using any auxiliary data, is robust in the sense that it does not depend on the distribution of outcome variables and the prior.
