This paper outlines a methodology for semi-parametric spatio-temporal modelling of data which is dense in time but sparse in space, obtained from a split panel design, the most feasible approach to covering space and time with limited equipment. The data are hourly averaged particle number concentration (PNC) and were collected, as part of the Ultrafine Particles from Transport Emissions and Child Health (UPTECH) project. Two weeks of continuous measurements were taken at each of a number of government primary schools in the Brisbane Metropolitan Area. The monitoring equipment was taken to each school sequentially. The school data are augmented by data from long term monitoring stations at three locations in Brisbane, Australia. Fitting the model helps describe the spatial and temporal variability at a subset of the UPTECH schools and the long-term monitoring sites. The temporal variation is modelled hierarchically with penalised random walk terms, one common to all sites and a term accounting for the remaining temporal trend at each site. Parameter estimates and their uncertainty are computed in a computationally efficient approximate Bayesian inference environment, R-INLA. The temporal part of the model explains daily and weekly cycles in PNC at the schools, which can be used to estimate the exposure of school children to ultrafine particles (UFPs) emitted by vehicles. At each school and long-term monitoring site, peaks in PNC can be attributed to the morning and afternoon rush hour traffic and new particle formation events. The spatial component of the model describes the school to school variation in mean PNC at each school and within each school ground. It is shown how the spatial model can be expanded to identify spatial patterns at the city scale with the inclusion of more spatial locations.

中文翻译：

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面板设计数据的贝叶斯时空模型：澳大利亚布里斯班的空气中颗粒数浓度

本文概述了一种对时间密集但空间稀疏的数据进行半参数时空建模的方法，该方法是从拆分面板设计中获得的，这是用有限的设备覆盖空间和时间的最可行方法。这些数据是每小时平均粒子数浓度 (PNC) 并收集，作为来自交通排放和儿童健康 (UPTECH) 项目的超细粒子的一部分。在布里斯班都会区的许多公立小学中，每所学校都进行了为期两周的连续测量。监控设备依次送到各学校。来自澳大利亚布里斯班三个地点的长期监测站的数据增强了学校数据。拟合模型有助于描述 UPTECH 学校子集和长期监测站点的空间和时间变化。时间变化是用惩罚随机游走项分层建模的，一个对所有站点通用的术语和一个解释每个站点剩余时间趋势的术语。参数估计及其不确定性在计算效率高的近似贝叶斯推理环境 R-INLA 中计算。模型的时间部分解释了学校 PNC 的每日和每周周期，可用于估计学龄儿童接触车辆排放的超细颗粒 (UFP) 的情况。在每个学校和长期监测站点，PNC 的高峰可归因于上午和下午的高峰时段交通和新的粒子形成事件。模型的空间组件描述了每所学校和每所校园内平均 PNC 的学校间差异。展示了如何扩展空间模型以识别包含更多空间位置的城市尺度的空间模式。