We implemented a spatial model for analysing ${\mathrm{PM}}_{10}$ maxima across the Mexico City metropolitan area during the period 1995–2016. We assumed that these maxima follow a non-identical generalized extreme value (GEV) distribution and modeled the trend by introducing multivariate smoothing spline functions into the probability GEV distribution. A flexible, three-stage hierarchical Bayesian approach was developed to analyse the distribution of the ${\mathrm{PM}}_{10}$ maxima in space and time. We evaluated the statistical model’s performance by using a simulation study. The results showed strong evidence of a positive correlation between the ${\mathrm{PM}}_{10}$ maxima and the longitude and latitude. The relationship between time and the ${\mathrm{PM}}_{10}$ maxima was negative, indicating a decreasing trend over time. Finally, a high risk of ${\mathrm{PM}}_{10}$ maxima presenting levels above 1000 $\mathsf{\mu }$ g/m ${}^3$ (return period: 25 yr) was observed in the northwestern region of the study area.

Dengue is a major public health concern mainly in tropical and subtropical environments worldwide. Despite several attempts to prevent this disease occurring in tropical regions of Mexico, it has not yet been controlled. This work focused on spatial modeling of confirmed dengue fever cases that occurred during the period 2010–2014 in the Huasteca Potosina region of Mexico. Multivariable Logistic Regression Modeling (MLRM) was used to determine the relationship between explanatory variables and the presence/absence of dengue. Model performance was evaluated using the area under curve (AUC) of the relative operating characteristic (ROC); AUC > 0.95. A high spatial resolution map was created to reveal the most probable patterns of dengue risk. Our results can be used for targeted control and prevention programs at local and regional levels. This methodology can be applied to other major diseases that are spatially distributed in accordance with environmental factors.

We introduce a novel spatial model based on the distribution of generalized extreme values (GEVs) and tree ensemble models to analyze the maximum concentrations levels of particulate matter with a diameter of less than 2.5 microns (PM2.5) in the Mexico City metropolitan area during the period 2003–2021. Spatial trends were modeled through a decision tree in the context of a non-stationary GEV model. We used a tree ensemble model as a predictor of GEV parameters to approximate nonlinear trends. The decision tree was built by using a greedy stagewise approach, the objective function of which was the log-likelihood. We verified the validity of our model by means of the likelihood and Akaike’s information criterion (AIC). The maps of the generalized extreme value parameters on the spatial plane show the existence of differentiated local trends in the extreme values of PM2.5 in the study area. The results indicated strong evidence of an increase in the west–east direction of the study area. A spatial map of risk with maximum concentration levels of PM2.5 in a period of 25 years was built.