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的观察)或最优顺序分配规则(用于将更多的受试者分配到治疗)，可以降低实验的预期成本。对所得估计量的抽样分布的困难分析将使用更新理论和由于渐近展开而产生的近似。这些展开式也产生对后验分布的近似，并用于逼近最优贝叶斯设计。序贯估计方法将被应用于校准问题以及非参数固定宽度的可信区间。

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.