The design of experiments for discriminating between two rival models
The design of experiments for discriminating between two rival models
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区分两个竞争模型的实验设计
DOI：
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发表时间：
1975
期刊：
影响因子：
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通讯作者：
V. Fedorov
中科院分区：
文献类型：
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作者：
A. Atkinson;V. Fedorov
其中设计点 xi 已知，随机变量 Cik 独立正态分布，均值为零，方差为 0y2。在理论发展中，而不是在数值例子中，为了不失一般性，我们将取0-2作为统一。函数 st(x) 是两个已知函数 81(x, 01) 和 82(x, 02) 之一，其中 01 和 02 是维度 m1 和 in2 的未知参数集。实验的目的是确定这两个模型中哪一个是正确的。几位作者已经研究了用于区分任意数量模型的实验设计。 Atkinson & Cox (1974) 最近的论文以及随后的讨论中给出了对这项工作的参考以及对该问题的一般方面的一些评论。 Fedorov & Malyutov (1972) 和 Fedorov & Uspensky (1975) 导出了专门用于区分两个模型的设计。在本文中，我们收集、举例说明并概括了两个模型的设计结果，并描述了与 Atkinson & Cox 设计的关系，这些设计基于 D 最优设计理论的扩展。在 ？ 2 我们描述了非顺序设计，哪些是顺序设计的限制？ 3随着试验次数的增加而收敛。在 ？在图 4 中，我们讨论了当两个模型都是线性时两种方法之间的关系。两个模型中参数的最小二乘估计（通常不需要是线性的）是方程的解
where the design points xi are known and the random variables Cik are independently normally distributed with zero mean and constant variance 0y2. In the theoretical development, but not in the numerical examples, we shall, without loss of generality, take 0-2 to be unity. The function st(x) is one of two known functions 81(x, 01) and 82(x, 02), where 01 and 02 are sets of unknown parameters of dimension m1 and in2. The purpose of the experiment is to determine which of the two models is true. The design of experiments for discriminating between any number of models has been investigated by several authors. References to this work and some comments on general aspects of the problem are given in the recent paper of Atkinson & Cox (1974) and in the ensuing discussion. Designs specific for discriminating between only two models have been derived by Fedorov & Malyutov (1972) and Fedorov & Uspensky (1975). In the present paper we collect, exemplify and generalize these results on designs for two models and describe the relationship with the designs of Atkinson & Cox, which are based on an extension of D-optimum design theory. In ? 2 we describe nonsequential designs which are the limits to which the sequential designs of ? 3 converge as the number of trials increases. In ? 4 we discuss the relationship between the two approaches when both models are linear. The least squares estimates of the parameters in the two models, which in general need not be linear, are the solutions of the equations