Simultaneous Bayesian Sequential Estimation
研究了在多个子总体中同时进行贝叶斯序贯估计的问题，提出了两种抽样方案下的最优估计程序，并比较了它们的期望总成本。
Abstract Suppose a population is composed of I ≥ 2 distinct subpopulations, where πi > 0 is the proportion of the population in the ith subpopulation, i = 1, …, I. Given θi, 0 < θi < 1, a sequence of independent Bernoulli (θi) random variables can be observed from the ith subpopulation that are also independent across subpopulations. Of interest is the simultaneous Bayes sequential estimation of θ1, …, θ1, using component loss and linear sampling cost. The estimation problem is solved under two sampling schemes. The first scheme requires that at each stage one observation be taken from the entire population without controlling the subpopulation sampled. The second scheme requires that at each stage one observation be taken from each subpopulation. The Bayes sequential estimation procedures are found for both schemes and compared in terms of expected total cost. These results are then extended from Bernoulli trials to a one-parameter exponential family with mean θi and component loss , where varθ iU is the ith subpopulation variance.