For estimation and predictions of random fields, it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for empirical kriging (EK) are then often non-space-filling and very costly to determine. In this paper, we investigate the possibility of using a compound criterion inspired by an equivalence theorem type relation to build designs quasi-optimal for the EK variance when space-filling designs become unsuitable. Two algorithms are proposed, one relying on stochastic optimization to explicitly identify the Pareto front, whereas the second uses the surrogate criteria as local heuristic to choose the points at which the (costly) true EK variance is effectively computed. We illustrate the performance of the algorithms presented on both a simple simulated example and a real oceanographic dataset. © 2014 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.

中文翻译：

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随机场的有效预测设计

对于随机场的估计和预测，人们越来越认识到克里金方差可能无法代表真正的不确定性。基于适用于经验克里金法 (EK) 的更详细标准的实验设计通常是非空间填充的，并且确定成本非常高。在本文中，我们研究了在空间填充设计变得不合适时，使用受等价定理类型关系启发的复合标准来构建对 EK 方差准最优的设计的可能性。提出了两种算法，一种依靠随机优化来明确识别帕累托前沿，而第二种使用替代标准作为局部启发式来选择有效计算（昂贵的）真实 EK 方差的点。我们在一个简单的模拟示例和一个真实的海洋数据集上展示了算法的性能。© 2014 作者。John Wiley & Sons, Ltd. 出版的《商业和工业中的应用随机模型》。