二元响应数据的有效初始设计
Efficient initial designs for binary response data
摘要：
在本文中，我们介绍了一个二进制搜索算法，有效地找到初始最大似然估计的连续实验，其中二进制响应是由一个连续的因素。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，电流是由实验者控制的因素，并且测量指示电压响应的存在或不存在的二进制响应。模型参数的先验知识通常很贫乏，这可能导致常用的初始估计方法失效。二叉搜索算法被设计为即使在先验信息非常差的情况下也能可靠地工作。该算法的性能进行了研究，在模拟和优势的初始估计与等间隔的因素水平被证明。我们还研究了二进制搜索算法的成本效率，并找到近似最佳的测量每阶段的数量时，有一个成本相关的实验中的阶段数。关键词：最优设计，二分搜索，逻辑斯谛回归，互补重对数，量子物理，开关测量
英文摘要：
In this paper we introduce a binary search algorithm that efficiently finds initial maximum likelihood estimates for sequential experiments where a binary response is modeled by a continuous factor. The problem is motivated by switching measurements on superconducting Josephson junctions. In this quantum mechanical experiment, the current is the factor controlled by the experimenter and a binary response indicating the presence or the absence of a voltage response is measured. The prior knowledge on the model parameters is typically poor, which may cause the common approaches of initial estimation to fail. The binary search algorithm is designed to work reliably even when the prior information is very poor. The properties of the algorithm are studied in simulations and an advantage over the initial estimation with equally spaced factor levels is demonstrated. We also study the cost-efficiency of the binary search algorithm and find the approximately optimal number of measurements per stage when there is a cost related to the number of stages in the experiment. KEY WORDS: optimal design, binary search, logistic regression, complementary log-log, quantum physics, switching measurement
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