Algorithmic Searches for Optimal Designs
Algorithmic Searches for Optimal Designs
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最佳设计的算法搜索
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Yaming Yu
中科院分区：
文献类型：
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作者：
A. Mandal;W. Wong;Yaming Yu
对最佳实验设计的研究有着悠久的历史，可以追溯到1918年初史密斯（1918）的一篇开创性论文，可能更早。本章讨论在给定设计空间上定义的统计模型中寻找最佳设计的算法。我们讨论了背景和需要的算法，以找到一个最优设计的各种情况。文献中有不同类型的算法，即使对于相同的设计问题，研究人员通常也有几种算法可供选择以找到最优设计。还有一些算法使用专门的方法为非常具体的应用程序找到最佳设计。例如，赛义德。（2011）使用数学规划技术使用环切分集搜索d -最优设计。因此，关于为统计模型寻找最佳设计的算法的文献是巨大而多样的。本章的目的是简要概述寻找最佳设计的算法，并讨论代表一些当前趋势的选定算法。我们还强调了更广泛适用于解决不同类型设计问题的算法。我们讨论了在使用算法方法寻找最佳设计时遇到的典型问题，并提出了来自其他领域的替代算法，这些算法似乎能够快速轻松地为研究中的任何模型和目标生成有效的设计。在此过程中，我们为其中一些算法提供伪代码，并说明它们如何解决生物医学中实际和当前的设计问题。近年来，实验成本在许多层面上急剧上升，研究人员越来越希望在不牺牲统计推断质量的情况下最小化研究成本。即使不考虑成本因素，设计问题仍然非常重要。这是因为一个糟糕的设计可能会提供不可靠的答案，要么是因为估计有不可接受的大方差，要么是因为它在科学研究中为检验主要假设提供了低功率。在极端的情况下，当研究设计得如此糟糕时，无论样本量有多大，它甚至可能无法为感兴趣的主要科学问题提供答案。因此，所有的研究都应在开始时仔细计划。必须事先明确指定主要目标，以及与实验执行和解释相关的所有模型假设、约束和实际问题。通常，制定一个称为设计最优性准则的数学函数，以尽可能准确地反映研究的目标。常见的标准是D-
Research in optimal experimental design has a long history and dates back as early 1918 in a seminal paper by Smith (1918) and probably earlier. This chapter discusses algorithms for finding an optimal design given a statistical model defined on a given design space. We discuss background and the need for algorithms to find an optimal design for various situations. There are different types of algorithms available in the literature and even for the same design problem, the researcher usually has several algorithms to choose from to find an optimal design. There are also algorithms that use specialized methods to find an optimal design for a very specific application. For example, Syed el at. (2011) used a mathematical programming technique to search for a D-optimal design using cyclotomic cosets. The literature on algorithms to find an optimal design for a statistical model is therefore huge and diverse. The aim of this chapter is to give a brief overview on algorithms for finding optimal designs and to discuss selected algorithms that represent some of the current trends. We also highlight algorithms that are more widely applicable for solving different types of design problems. We discuss typical problems encountered in using an algorithmic approach to find an optimal design and present alternative algorithms from other fields that seem capable of generating efficient designs quickly and easily for any model and objective in the study. Along the way, we provide pseudo-codes for some of these algorithms and illustrate how they work to solve real and current design problems in biomedicine. In recent years, experimental costs have risen steeply at many levels and researchers increasingly want to minimize study costs without having to sacrifice the quality of the statistical inference. Even with cost considerations aside, design issues are still very important. This is because a poor design can provide unreliable answers either because the estimates have unacceptably large variances or it provides low power for testing the main hypothesis in the scientific study. In the extreme case, when the study is so badly designed, it may not even provide an answer to the main scientific question of interest no matter how large the sample size is. Thus all studies should be carefully planned at the onset. The main goal or goals have to be clearly specified in advance, along with all model assumptions, constraints and practical concerns associated with execution and interpretation of the experiment. Typically, a mathematical function called a design optimality criterion is formulated to reflect the objectives of the study as accurately as possible. A common criterion is D-
异方差多项式模型中预先指定区间的最优极小极大设计。
影响因子：
0.8
作者：
Chen,Ray-Bing;Wong,WengKee;Li,Kun-Yu
通讯作者：
Li,Kun-Yu