应用于切换测量的二元响应模型的近似成本有效序贯设计
Approximate cost-efficient sequential designs for binary response models with application to switching measurements
摘要：
试验设计的效率最终是以试验所需的时间和资源来衡量的。研究了每一阶段费用固定的最优序贯（多阶段）设计问题。这个问题是由超导约瑟夫森结的开关测量引起的。在这个量子力学实验中，将电流脉冲序列施加到约瑟夫森结样品上，并测量指示电压响应存在或不存在的二进制响应。二进制响应可以通过具有互补对数-对数连接函数的广义线性模型来建模。考虑的其他模型是logit模型和概率单位模型。对于这三个模型，作为当前Fisher信息和阶段成本的函数的下一阶段的近似最优样本量被确定。所提出的设计的成本效益证明在模拟开关测量的实际数据的基础上。结果可以直接应用到开关测量，他们可能会导致大量节省所需的实验时间。
英文摘要：
The efficiency of an experimental design is ultimately measured in terms of time and resources needed for the experiment. Optimal sequential (multi-stage) design is studied in the situation where each stage involves a fixed cost. The problem is motivated by switching measurements on superconducting Josephson junctions. In this quantum mechanical experiment, the sequences of current pulses are applied to the Josephson junction sample and a binary response indicating the presence or the absence of a voltage response is measured. The binary response can be modeled by a generalized linear model with the complementary log-log link function. The other models considered are the logit model and the probit model. For these three models, the approximately optimal sample size for the next stage as a function of the current Fisher information and the stage cost is determined. The cost-efficiency of the proposed design is demonstrated in simulations based on real data from switching measurements. The results can be directly applied to switching measurements and they may lead to substantial savings in the time needed for the experiment.
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