The last decade has seen an explosion in data sources available for the monitoring and prediction of environmental phenomena. While several inferential methods have been developed that make predictions on the underlying process by combining these data, an optimal sampling design for when additional data is needed to complement those from other heterogeneous sources has not yet been developed. Here, we provide an adaptive spatial design strategy based on a utility function that combines both prediction uncertainty and risk-factor criteria. Prediction uncertainty is obtained through a spatial data fusion approach based on fixed rank kriging that can tackle data with differing spatial supports and signal-to-noise ratios. We focus on the application of low-cost portable sensors, which tend to be relatively noisy, for air pollution monitoring, where data from regulatory stations as well as numeric modeling systems are also available. Although we find that spatial adaptive sampling designs can help to improve predictions and reduce prediction uncertainty, low-cost portable sensors are only likely to be beneficial if they are sufficient in number and quality. Our conclusions are based on a multi-factorial simulation experiment, and on a realistic simulation of pollutants in the Erie and Niagara counties in Western New York.

翻译：过去十年间，用于环境现象监测与预测的数据源呈爆炸式增长。尽管已有多种推断方法通过整合这些数据对潜在过程进行预测，但针对需要补充其他异质数据源的优化采样设计尚未形成。本文提出一种基于效用函数的自适应空间设计策略，该函数融合了预测不确定性与风险因子准则。预测不确定性通过基于固定秩克里金法的空间数据融合方法获得，该方法能处理具有不同空间支撑和信噪比的数据。我们重点关注低成本便携式传感器（通常噪声较大）在空气污染监测中的应用，同时整合了监管站点与数值模型系统的数据。尽管研究发现自适应空间采样设计有助于改进预测并降低预测不确定性，但低成本便携式传感器仅在其数量与质量达到足够水平时才可能发挥效益。结论基于多因素仿真实验及对纽约州西部伊利县和尼亚加拉县污染物的真实情景模拟得出。