贝叶斯时空分位回归模型及其对北京市PM2.5浓度的研究

Bayesian Spatio-temporal Quantile Regression Model and its Application in PM2.5 Concentration in Beijing

本文基于时空模型和非对称拉普拉斯分布提出一种新的时空分位回归模型。本文主要将空间域利用薄板回归样条展开,结合混合模型与样条之间的关系,得到分层贝叶斯分位回归模型。利用MCMC算法得到参数的后验分布,并对模型中系数的空间域进行预测。本文同时融合降秩近似的方法,简化了计算复杂度。区别于已有时空分位模型,本文考虑了协变量对因变量影响的空间分布特征,并非直接对时间或空间效应整体进行建模,有利于深入研究协变量与因变量之间的空间结构关系。数值模拟结果表明,预测的空间域与真实的空间域十分接近,并在不同分位水平下,有效地估计了协变量影响的空间效应差异。最后将该模型应用于北京市PM2.5浓度的研究,分析气象因素对PM2.5浓度影响的空间分布特征。

Based on the spatio-temporal model and asymmetric Laplace distribution, this paper proposes a new spatiotemporal quantile regression model. In this article, the spatial fields are expanded by Thin Plate Regression Spline, combining with the relationship between the mixed model and splines, we derive the hierarchical Bayesian quantile regression model. Using MCMC algorithm, we get the posterior distributions of unknown parameters, then the predictions of spatial fields are carried out. Besides, computational complexity is alleviated by rank-reducing method. Different from the existed spatio-temporal quantile models, we model the relationship between response and covariates, rather than the whole effects of spatial or temporal terms, which is helpful to study the spatial structure between interested variable and others related. Simulation results show that the predictions of spatial fields is very closed to their real values. Additionally, under different quantiles, the model could effectively estimate the difference between quantile effects. Finally, we apply our model to the concentration of PM2. 5 in Beijing, analyzing the spatially distributional characters of the meteorological variables＇ effects on PM2. 5.