AI 中文总结
该研究针对空间相关功能数据，提出带正则化马蹄先验的小波贝叶斯分层模型，能稳定预测未监测位置的污染物曲线及不确定性，在墨西哥城PM₁₀数据上表现优于对比方法。
AI 中文摘要
环境监测网络日益将污染物水平记录为固定站点随时间观测的曲线，但暴露与风险评估常需要在未监测位置预测这些曲线及其不确定性。针对这类空间相关功能数据的传统光滑基方法，包括基于样条的克里金法，往往会过度平滑尖锐、高频的事件，如污染峰值。我们提出一种简约的基于小波的贝叶斯分层模型，该模型在每个分辨率级别锚定单一共享的Matérn相关矩阵，避免了系数特定空间过程的参数膨胀。通过空间信息正则化马蹄先验实施自适应稀疏性，使模型能在相邻位置间借用强度，同时，非中心化参数化确保在No-U-Turn采样器下的稳定推断。在不同信噪比 regime 的模拟研究中，与严格独立模型相比，纳入空间依赖性在严重噪声下大幅稳定了重构效果。将模型应用于墨西哥城的PM₁₀浓度数据，并与功能数据普通克里金法及分层贝叶斯小波替代模型对比，该模型能捕捉急性污染事件，且除了改善点预测外，还在未观测位置提供更尖锐、校准更好的可信区间。
英文摘要
Environmental monitoring networks increasingly record pollutant levels as curves observed over time at fixed stations. Yet, exposure and risk assessment often require predicting these curves, with their uncertainty, at unmonitored locations. Conventional smooth-basis methods for such spatially correlated functional data, including spline-based kriging, tend to over-smooth acute, high-frequency episodes such as pollution peaks. We propose a parsimonious wavelet-based Bayesian hierarchical model that anchors a single, shared Matérn correlation matrix at each resolution level, avoiding the parameter inflation of coefficient-specific spatial processes. Adaptive sparsity is enforced through a spatially informed regularized horseshoe prior, allowing the model to borrow strength across neighboring locations. At the same time, a non-centered parameterization ensures stable inference under the No-U-Turn Sampler. In simulation studies across distinct signal-to-noise regimes, incorporating spatial dependence substantially stabilizes reconstruction under severe noise relative to strictly independent models. Applied to PM$_{10}$ concentrations from Mexico City and benchmarked against ordinary kriging for functional data and a hierarchical Bayesian wavelet alternative, the model captures acute pollution events and, beyond improving point prediction, delivers sharper and better-calibrated credible intervals at unobserved locations.
