Acquiring information on spatial phenomena can be costly and time-consuming. In this context, to obtain reliable global knowledge, the choice of measurement location is a crucial issue. Space-lling designs are often used to control variability uniformly across the whole space. However, in a monitoring context, it is more relevant to focus on crucial regions, especially when dealing with sensitive areas such as the environment, climate or public health. It is therefore important to choose a relevant optimality criterion to build models adapted to the purpose of the experiment. In this article, we propose two new optimality criteria: the rst aims to focus on areas where the response exceeds a given threshold, while the second is suitable for estimating sets of levels. We introduce several algorithms for constructing optimal designs. We also focus on cost-eective algorithms that produce non-optimal but ecient designs. For both sequential and non-sequential contexts, we compare our designs with existing ones through extensive simulation studies.

翻译：获取空间现象的信息可能成本高昂且耗时。在此背景下，为获得可靠的全局认知，测量位置的选择至关重要。空间填充设计常被用于在整个空间内均匀控制变异性。然而，在监测场景中，尤其是涉及环境、气候或公共卫生等敏感领域时，聚焦关键区域更为贴切。因此，选择相关的最优准则来构建适应实验目的模型尤为重要。本文提出两个新的最优准则：第一个旨在聚焦响应值超过给定阈值的区域，第二个适用于估计水平集。我们引入了多种构建最优设计的算法，同时着重关注能生成非最优但高效设计的成本效益算法。针对序贯与非序贯两种场景，我们通过大量仿真研究，将所提出的设计方法与现有方法进行了比较。