Abstract Maximum entropy sampling (MES) criteria provide a useful framework for studying sequential designs for computer experiments in a Bayesian framework. However, there is some technical difficulty in making the procedure fully adaptive in the sense of making proper use of previous output as well as input data. In the simple Gaussian set-up only previous input values need to be used. The approach discussed uses a full hierarchical model for the Gaussian process. The idea is to take advantage of the Karhumen-Loéve (K-L) expansion to approximate the process covariance function using an orthogonal function basis. It is argued that this may make it easier to use Bayesian hierarchical models, rather than estimating the covariance parameters directly, using the traditional approach. The article paper shows how to reduce the full MES method to a simple one by using a special empirical Bayes approximation, rather than using time-consuming integration. A simple simulator example is presented to show that full adaptation is beneficial.

中文翻译：

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计算机实验自适应设计的探讨

摘要 最大熵采样 (MES) 标准为研究贝叶斯框架中计算机实验的顺序设计提供了一个有用的框架。然而，在正确使用以前的输出和输入数据的意义上使程序完全自适应存在一些技术困难。在简单的高斯设置中，只需要使用先前的输入值。所讨论的方法对高斯过程使用完整的分层模型。这个想法是利用 Karhumen-Loéve (KL) 扩展来使用正交函数基础来近似过程协方差函数。有人认为，这可能使使用贝叶斯分层模型更容易，而不是使用传统方法直接估计协方差参数。文章论文展示了如何通过使用特殊的经验贝叶斯近似而不是使用耗时的积分将完整的 MES 方法简化为简单的方法。提供了一个简单的模拟器示例以表明完全适应是有益的。