Very unhealthy air quality is consistently connected with numerous diseases. Appropriate extreme analysis and accurate predictions are in rising demand for exploring potential linked causes and for providing suggestions for the environmental agency in public policy strategy. This paper aims to model the spatial and temporal pattern of both moderate and very poor PM10 concentrations collected from 342 representative monitors distributed throughout mainland Spain from 2017 to 2021. We firstly propose and compare a series of Bayesian generalized extreme models of annual maxima PM10 concentrations, including both the fixed effect as well as the spatio-temporal random effect with the Stochastic Partial Differential Equation approach and a lag-one dynamic auto-regressive component. The similar and different effects of interrelated factors are identified through a joint Bayesian model of annual mean and annual maxima PM10 concentrations, which may bring the power of statistical inference of body data to the tail analysis with implementation in the faster and more accurate Integrated Nested Laplace Approximation (INLA) algorithm with respect to MCMC. Under WAIC, DIC and other criteria, the best model is selected with good predictive ability based on the first four-year data for training and the last-year data for testing. The findings are applied to identify the hot-spot regions with extremely poor quality using excursion functions specified at the grid level. It suggests that the community of Madrid and the northwestern boundary of Spain are likely to be exposed to severe air pollution simultaneously exceeding the warning risk threshold. The joint model also provides evidence that certain predictors (precipitation, vapour pressure and population density) influence comparably while the other predictors (altitude and temperature) impact oppositely in the different scaled PM10 concentrations.

翻译：极度不健康的空气质量一直与多种疾病密切相关。针对潜在关联原因的探索以及为环境机构制定公共政策策略提供建议，对极端值分析和精准预测的需求日益增长。本文旨在对2017年至2021年西班牙本土分布的342个代表性监测站点采集的中度和极差PM10浓度进行时空模式建模。我们首先提出并比较了一系列年度最大PM10浓度的贝叶斯广义极值模型，包括固定效应、基于随机偏微分方程方法的时空随机效应以及一阶滞后动态自回归分量。通过年度均值与年度最大PM10浓度的联合贝叶斯模型，识别出相互关联因素的相似与差异效应，这可将主体数据的统计推断能力引入尾部分析，并采用比MCMC更快更准确的集成嵌套拉普拉斯逼近算法实现。在WAIC、DIC等准则下，基于前四年数据训练、最后一年数据测试，选出具有良好预测能力的最优模型。研究结果通过网格级设定的离差函数识别出空气质量极差的热点区域，表明马德里社区及西班牙西北边界区域可能同时遭受超过预警风险阈值的严重空气污染。联合模型还提供证据表明，某些预测因子（降水量、水汽压和人口密度）对不同尺度的PM10浓度影响相似，而其他预测因子（海拔和温度）则呈现相反影响。