Mathematical Sciences: Stopping and Allocation

实验的预期成本可以通过以下方式降低： 使用最佳停止规则（用于决定是否 以进行进一步的观察）或最优顺序分配 规则（用于分配更多受试者接受治疗）。 的 很难分析结果的抽样分布 估计将受到攻击，使用更新理论和 由于渐近展开的近似。 这些扩张 也产生后验分布的近似值， 用于近似最优贝叶斯设计。 顺序 估计方法将被应用于校准问题 以及非参数固定宽度置信区间。

The expected cost of an experiment can be reduced through the use of an optimal stopping rule (for deciding whether or not to make further observations) or an optimal sequential allocation rule (for assignment of further subjects to treatments). The difficult analysis of the sampling distribution of the resulting estimators will be attacked using renewal theory and approximations due to asymptotic expansions. These expansions also yield approximations to posterior distributions and are of use in approximating optimal Bayesian designs. Sequential methods of estimation will be applied to the calibration problem as well as nonparametric fixed width confidence intervals.