Rapid developments in streaming data technologies have enabled real-time monitoring of human activity that can deliver high-resolution data on health variables over trajectories or paths carved out by subjects as they conduct their daily physical activities. Wearable devices, such as wrist-worn sensors that monitor gross motor activity, have become prevalent and have kindled the emerging field of ``spatial energetics'' in environmental health sciences. We devise a Bayesian inferential framework for analyzing such data while accounting for information available on specific spatial coordinates comprising a trajectory or path using a Global Positioning System (GPS) device embedded within the wearable device. We offer full probabilistic inference with uncertainty quantification using spatial-temporal process models adapted for data generated from ``actigraph'' units as the subject traverses a path or trajectory in their daily routine. Anticipating the need for fast inference for mobile health data, we pursue exact inference using conjugate Bayesian models and employ predictive stacking to assimilate inference across these individual models. This circumvents issues with iterative estimation algorithms such as Markov chain Monte Carlo. We devise Bayesian predictive stacking in this context for models that treat time as discrete epochs and that treat time as continuous. We illustrate our methods with simulation experiments and analysis of data from the Physical Activity through Sustainable Transport Approaches (PASTA-LA) study conducted by the Fielding School of Public Health at the University of California, Los Angeles.

翻译：流式数据技术的快速发展使得对人类活动的实时监测成为可能，能够提供受试者在日常体力活动中沿轨迹或路径行进时健康变量的高分辨率数据。可穿戴设备（例如监测总体运动活动的手腕传感器）已变得普遍，并催生了环境健康科学中新兴的“空间能量学”领域。我们设计了一个贝叶斯推断框架来分析此类数据，同时利用嵌入可穿戴设备中的全球定位系统（GPS）设备，对构成轨迹或路径的特定空间坐标的可用信息进行建模。我们采用适用于“活动记录仪”单元生成数据的时空过程模型，在受试者日常活动中穿越路径或轨迹时，提供具有不确定性量化的完整概率推断。考虑到移动健康数据对快速推断的需求，我们采用共轭贝叶斯模型进行精确推断，并利用预测堆叠来整合这些个体模型的推断结果。这避免了马尔可夫链蒙特卡罗等迭代估计算法的问题。我们在此背景下针对将时间视为离散时段和连续时间的模型，设计了贝叶斯预测堆叠方法。我们通过模拟实验以及对加州大学洛杉矶分校菲尔丁公共卫生学院开展的“通过可持续交通方式促进体力活动（PASTA-LA）”研究数据的分析，来阐述我们的方法。