Spatially referenced datasets have become increasingly prevalent across many fields, largely driven by advances in data collection methods such as satellite remote sensing. In many applications, predictions at unobserved locations are accompanied by reliable uncertainty estimates. While deep learning methods provide both scalable and accurate models for spatial predictions, there remains no clear consensus for addressing uncertainty quantification in spatial deep learning. Monte Carlo (MC) dropout has become a popular approach for uncertainty quantification, yet existing implementations typically focus on tuning the dropout rate while fixing other influential hyperparameters, such as weight decay and the predictive standard deviation multiplier, often through ad-hoc or manual tuning. We propose a cubing-based diagnostic framework that recursively partitions the hyperparameter space to identify stable regions where MC dropout yields well-calibrated predictive intervals. The approach evaluates hyperparameter regions using scoring rules relative to a statistical baseline model, which serves as a calibration anchor. Through a simulation study spanning multiple spatial dependence regimes as well as a large remotely-sensed land surface temperature dataset, we demonstrate that our approach produces competitive or superior predictive intervals compared to the baseline model. Our methodology provides practitioners with a systematic procedure for incorporating uncertainty quantification into spatial deep learning models.

翻译：空间参考数据集已日益普及于众多领域，这主要得益于数据采集方法的进步，如卫星遥感。在许多应用中，对未观测位置的预测需伴随可靠的置信度估计。尽管深度学习方法为空间预测提供了可扩展且精确的模型，但关于如何在空间深度学习中处理不确定量化仍缺乏明确共识。蒙特卡洛（MC）丢弃法已成为一种流行的不确定量化方法，然而现有实现通常侧重于调整丢弃率，同时固定其他影响超参数，如权重衰减和预测标准差乘子，往往通过临时或手动调整进行。我们提出了一种基于立方体的诊断框架，该框架递归地划分超参数空间，以识别MC丢弃法能够产生良好校准预测区间的稳定区域。该方法利用相对于统计基线模型（作为校准锚定）的评分规则来评估超参数区域。通过涵盖多种空间依赖机制的大规模模拟研究以及一个大型遥感地表温度数据集，我们证明了该方法能产生与基线模型相比具有竞争力或更优的预测区间。我们的方法为实践者提供了一种系统性程序，以将不确定量化融入空间深度学习模型。