Asymptotically Optimal Bayes Sequential Design of Experiments for Estimation

Abstract

The purpose of this paper is to find asymptotically optimal Bayes sequential procedures for estimating a function $g(\theta_1, \theta_2,\cdots, \theta_k)$ when there are $k$ experiments $E_1, E_2,\cdots, E_k$ and the performance of the experiment $E_i$ conducts to the observation of a random variable whose distribution depends on the vector parameter $\theta_i$. The term asymptotical refers here to the cost of experimentation tending to zero. The methods used are a generalization of those introduced by Bickel and Yahav.