Abstract We consider the problem of estimating the set of all inputs that leads a system to some particular behavior. The system is modeled by an expensive-to-evaluate function, such as a computer experiment, and we are interested in its excursion set, that is, the set of points where the function takes values above or below some prescribed threshold. The objective function is emulated with a Gaussian process (GP) model based on an initial design of experiments enriched with evaluation results at (batch-) sequentially determined input points. The GP model provides conservative estimates for the excursion set, which control false positives while minimizing false negatives. We introduce adaptive strategies that sequentially select new evaluations of the function by reducing the uncertainty on conservative estimates. Following the stepwise uncertainty reduction approach we obtain new evaluations by minimizing adapted criteria. Tractable formulas for the conservative criteria are derived, which allow more convenient optimization. The method is benchmarked on random functions generated under the model assumptions in different scenarios of noise and batch size. We then apply it to a reliability engineering test case. Overall, the proposed strategy of minimizing false negatives in conservative estimation achieves competitive performance both in terms of model-based and model-free indicators. Supplementary materials for this article are available online.

中文翻译：

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偏移集保守估计实验的自适应设计

摘要 我们考虑估计导致系统某些特定行为的所有输入的集合的问题。该系统由评估成本高昂的函数（例如计算机实验）建模，我们对其偏移集感兴趣，即函数取值高于或低于某个规定阈值的点集。目标函数用高斯过程 (GP) 模型模拟，该模型基于实验的初始设计，在（批量）顺序确定的输入点处富含评估结果。GP 模型为偏移集提供了保守估计，它控制了误报，同时最大限度地减少了漏报。我们引入了自适应策略，通过减少保守估计的不确定性，依次选择新的函数评估。遵循逐步降低不确定性的方法，我们通过最小化适应的标准来获得新的评估。推导出了保守标准的易处理公式，可以更方便地进行优化。该方法以模型假设下在噪声和批量大小的不同场景下生成的随机函数为基准。然后我们将其应用于可靠性工程测试用例。总体而言，所提出的在保守估计中最小化假阴性的策略在基于模型和无模型指标方面都实现了竞争性能。本文的补充材料可在线获取。该方法以模型假设下在噪声和批量大小的不同场景下生成的随机函数为基准。然后我们将其应用于可靠性工程测试用例。总体而言，所提出的在保守估计中最小化假阴性的策略在基于模型和无模型指标方面都实现了竞争性能。本文的补充材料可在线获取。该方法以模型假设下在噪声和批量大小的不同场景下生成的随机函数为基准。然后我们将其应用于可靠性工程测试用例。总体而言，所提出的在保守估计中最小化假阴性的策略在基于模型和无模型指标方面都实现了竞争性能。本文的补充材料可在线获取。