Model-based geostatistical design involves the selection of locations to collect data to minimise an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which, for geostatistical studies, could be to minimise the prediction uncertainty at unobserved locations. In this paper, we propose a new approach to design such studies via a loss function derived through considering the entropy about the model predictions and the parameters of the model. The approach also includes a multivariate extension to generalised linear spatial models, and thus can be used to design experiments with more than one response. Unfortunately, evaluating our proposed loss function is computationally expensive so we provide an approximation such that our approach can be adopted to design realistically sized geostatistical studies. This is demonstrated through a simulated study and through designing an air quality monitoring program in Queensland, Australia. The results show that our designs remain highly efficient in achieving each experimental objective individually, providing an ideal compromise between the two objectives. Accordingly, we advocate that our approach could be adopted more generally in model-based geostatistical design.
翻译:以模型为基础的地理统计设计包括选择地点收集数据,以尽可能减少所有可能的地点的预期损失功能; 具体规定了损失功能,以反映数据收集的目的,对地质统计研究来说,这种目的可以是最大限度地减少未观测地点的预测不确定性; 在本文中,我们提出一种新的方法,通过考虑模型预测和模型参数的增缩功能得出的损失功能来设计这种研究; 这种方法还包括对通用线性空间模型的多变量扩展,从而可以用来设计不止一个反应的实验。 不幸的是,评估我们拟议的损失功能是计算成本很高的,因此我们提供了近似的方法,以便我们能够设计现实规模的地理统计研究。这通过模拟研究和在澳大利亚昆士兰州设计空气质量监测程序来证明。 研究结果表明,我们的设计在个别实现每个实验目标方面仍然非常有效,在两个目标之间提供了理想的折中。 因此,我们主张,我们的方法可以在基于模型的地理统计设计中更普遍地被采用。