Mathematical Sciences: Stopping and Allocation

通过使用最优停止规则（用于决定是否进行进一步观察）或最优顺序分配规则（用于分配进一步的受试者进行治疗），可以降低实验的预期成本。利用渐近展开式的更新理论和近似来解决估计量抽样分布分析的困难。这些展开也产生近似后验分布，并用于近似最优贝叶斯设计。序贯估计方法将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.