Data collected from arrays of sensors are essential for informed decision-making in various systems. However, the presence of anomalies can compromise the accuracy and reliability of insights drawn from the collected data or information obtained via statistical analysis. This study aims to develop a robust Bayesian optimal experimental design (BOED) framework with anomaly detection methods for high-quality data collection. We introduce a general framework that involves anomaly generation, detection and error scoring when searching for an optimal design. This method is demonstrated using two comprehensive simulated case studies: the first study uses a spatial dataset, and the second uses a spatio-temporal river network dataset. As a baseline approach, we employed a commonly used prediction-based utility function based on minimising errors. Results illustrate the trade-off between predictive accuracy and anomaly detection performance for our method under various design scenarios. An optimal design robust to anomalies ensures the collection and analysis of more trustworthy data, playing a crucial role in understanding the dynamics of complex systems such as the environment, therefore enabling informed decisions in monitoring, management, and response.

翻译：从传感器阵列中收集的数据对于各系统基于信息的决策至关重要。然而，异常的存在会损害从采集数据或通过统计分析获得的信息中提取洞察的准确性和可靠性。本研究旨在开发一个结合异常检测方法的鲁棒贝叶斯最优实验设计（BOED）框架，以实现高质量数据采集。我们提出一个通用框架，该框架在搜索最优设计时包含异常生成、检测和误差评分。通过两个综合性模拟案例研究验证了该方法：第一个案例采用空间数据集，第二个案例采用时空河流网络数据集。作为基线方法，我们采用了基于最小化误差的常用预测型效用函数。结果展示了在不同设计场景下，我们方法在预测准确性与异常检测性能之间的权衡。对异常具有鲁棒性的最优设计能够确保更可靠数据的采集与分析，在理解环境等复杂系统动力学中发挥关键作用，从而为监测、管理和响应中的知情决策提供支持。