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，能够获取受试者在日常体力活动中所经轨迹或路径上的健康变量高分辨率数据。可穿戴设备（如监测粗大运动活动的腕戴传感器）已广泛普及，并催生了环境健康科学中新兴的"空间能量学"领域。我们构建了一个贝叶斯推断框架，通过整合可穿戴设备内置全球定位系统（GPS）获取的轨迹或路径特定空间坐标信息，对此类数据进行分析。我们采用适配受试者日常活动路径轨迹中"活动记录仪"单元生成数据的时空过程模型，实现包含不确定性量化的完整概率推断。鉴于移动健康数据对快速推断的需求，我们利用共轭贝叶斯模型进行精确推断，并通过预测叠加整合这些独立模型的推断结果，从而规避马尔可夫链蒙特卡洛等迭代估计算法存在的问题。我们针对离散时间区间和连续时间两种模型分别设计了贝叶斯预测叠加方法。通过模拟实验及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）"研究数据分析，验证了所提方法的有效性。