Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

中文翻译：

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最佳实验设计：公式和计算


“如何最好地获取数据”的问题对于自然科学和社会科学、工程应用等领域的建模和预测至关重要。最佳实验设计（OED）将这些问题形式化，并创建计算方法来回答它们。本文对现代 OED 进行了系统调查，从经典设计理论的基础到复杂模型 OED 的当前研究。我们首先回顾用于制定 OED 问题的标准，从而编码执行实验的目标。我们强调贝叶斯和决策理论方法的灵活性，其中包含非常适合非线性和非高斯统计模型的基于信息的标准。然后我们讨论估计或限制这些设计标准的值的方法；由于强非线性、高参数维度、大的每个样本成本或模型隐式的设置，这一努力可能相当具有挑战性。一组互补的计算问题涉及用于寻找设计的优化方法；我们在观察选择的离散（组合）设置以及可以连续参数化精确设计的设置中讨论此类方法。最后，我们提出了顺序 OED 的新兴方法，这些方法构建了非短视的设计策略，而不是显式设计；这些方法自然地适应过去实验的结果，提出新的实验，同时寻求所有要进行的实验之间的协调。在整个过程中，我们强调了重要的开放性问题和挑战。