Bayesian optimal design of experiments is a well-established approach to planning experiments. Briefly, a probability distribution, known as a statistical model, for the responses is assumed which is dependent on a vector of unknown parameters. A utility function is then specified which gives the gain in information for estimating the true value of the parameters using the Bayesian posterior distribution. A Bayesian optimal design is given by maximising the expectation of the utility with respect to the joint distribution given by the statistical model and prior distribution for the true parameter values. The approach takes account of the experimental aim via specification of the utility and of all assumed sources of uncertainty via the expected utility. However, it is predicated on the specification of the statistical model. Recently, a new type of statistical inference, known as Gibbs (or General Bayesian) inference, has been advanced. This is Bayesian-like, in that uncertainty on unknown quantities is represented by a posterior distribution, but does not necessarily rely on specification of a statistical model. Thus the resulting inference should be less sensitive to misspecification of the statistical model. The purpose of this paper is to propose Gibbs optimal design: a framework for optimal design of experiments for Gibbs inference. The concept behind the framework is introduced along with a computational approach to find Gibbs optimal designs in practice. The framework is demonstrated on exemplars including linear models, and experiments with count and time-to-event responses.

翻译：贝叶斯优化实验设计是一种成熟的实验规划方法。简而言之，该方法假设响应服从一种概率分布（即统计模型），该分布依赖于一组未知参数向量。随后指定一个效用函数，以衡量使用贝叶斯后验分布估计参数真值所获得的信息增益。贝叶斯优化设计通过最大化效用关于联合分布（由统计模型和参数真值的先验分布共同定义）的期望来得到。该方法通过效用函数的设定考虑实验目标，并通过期望效用考虑所有假设的不确定性来源。然而，该方法的有效性依赖于统计模型的正确设定。近年来，一种名为吉布斯（或广义贝叶斯）推断的新型统计推断方法被提出。该方法类似于贝叶斯方法，用后验分布表示未知量的不确定性，但未必依赖于统计模型的设定。因此，所得推断对统计模型误设的敏感性较低。本文旨在提出吉布斯优化设计：一种面向吉布斯推断的实验优化设计框架。本文介绍了该框架的核心概念，并给出一种在实践寻找吉布斯优化设计的计算方法。该框架通过线性模型以及计数响应和时间事件响应实验等示例进行了验证。