Optimal design facilitates intelligent data collection. In this paper, we introduce a fully Bayesian design approach for spatial processes with complex covariance structures, like those typically exhibited in natural ecosystems. Coordinate Exchange algorithms are commonly used to find optimal design points. However, collecting data at specific points is often infeasible in practice. Currently, there is no provision to allow for flexibility in the choice of design. We also propose an approach to find Bayesian sampling windows, rather than points, via Gaussian process emulation to identify regions of high design efficiency across a multi-dimensional space. These developments are motivated by two ecological case studies: monitoring water temperature in a river network system in the northwestern United States and monitoring submerged coral reefs off the north-west coast of Australia.

翻译：最佳设计有利于智能数据收集。在本文中,我们为具有复杂共变结构的空间过程引入了完全的巴伊西亚设计方法,这些过程与自然生态系统通常展示的一样,具有复杂的共变结构。协调交换算法通常用于寻找最佳设计点。然而,在具体地点收集数据在实践中往往不可行。目前,没有允许灵活选择设计的条款。我们还提议采用一种方法,通过高山进程模拟找到巴伊西亚取样窗口,而不是点点,以确定多维空间的设计效率高的区域。这些发展是由两个生态案例研究推动的:监测美国西北部河流网络系统的水温,以及监测澳大利亚西北沿岸的淹没珊瑚礁。