Using a decision theoretic approach, we seek to minimize the Bayes risk that arises from using a squared error loss function. Although selecting the form of an optimal estimator is critical to solving this problem, the real difficulty lies in determining an optimal strategy for sampling from the two populations. The problem of optimal estimation reduces, therefore, to a problem of optimal allocation, which can be solved using dynamic programming. Similar programming techniques are utilized to evaluate properties of a number of ad hoc allocation strategies that might also be considered for use in this problem. Two sample polynomials are analyzed along with a number of examples indicating the effects of different prior parameters settings. The effects of differences between prior parameters used in the design and analysis stages of the experiment are also examined.

Keywords: nonlinear estimation, sequential design, robustness, myopic, hyperopic, dynamic programming, adaptive allocation, product, Bayesian, fault tolerance