The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics is the design of the locations of the monitoring stations for those environmental processes of interest. One particular design criterion for monitoring networks that tries to reduce the uncertainty about predictions of unseen processes is called the maximum-entropy design. However, this design criterion involves a hard optimization problem that is computationally intractable for large data sets. Previous work of Wang et al. (2017) examined a probabilistic model that can be implemented efficiently to approximate the underlying optimization problem. In this paper, we attempt to establish statistically sound tools for assessing the quality of the approximations.

人们日益认识到不利的人类健康状况与许多环境物质以及过程之间的关联，因此需要对其进行监控。环境统计中出现的一个重要问题是针对那些感兴趣的环境过程的监测站的位置设计。试图减少有关看不见的过程的预测的不确定性的一种特定的监视网络设计标准称为最大熵设计。但是，此设计标准涉及一个硬优化问题，对于大型数据集在计算上难以解决。王等人的先前工作。（2017）研究了一个概率模型，该模型可以有效实施以近似潜在的优化问题。在本文中，