Fixed and sequential designs for estimation in the exponential family with comparisons and applications to binomial proportions using beta priors

A sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family is adopted and compared with the best fixed design. Comparisons of sequential and best fixed designs for estimation of the difference between two Bernoulli proportions with beta priors are conducted. Results on the lower bound for the Bayes risk due to estimation and expected cost are presented and shown to be of first-order efficiency. Numerical comparisons for the Bernoulli distribution with beta priors are presented.