This work presents an alternative methodology for modeling the exceedances of national and international air quality standards for three pollutants ( \(PM_{2.5}\) , \(PM_{10}\) and ozone) in the cities of Bogotá and Medellín during the period 2018-2020. The proposed approach is based on Non-Homogeneous Poisson Processes (NHPP) with Bayesian parameter estimation, which allows for a more realistic representation of the temporal dynamics of pollution events. The model also incorporates change-points to identify significant alterations in pollution patterns, attributable to public policy, climatic phenomena, or restrictions related to the COVID-19 pandemic. This is the first time this methodology has been applied to data from the city of Medellín, and the results are compared with those obtained for Bogotá. The findings reveal substantial differences between the two cities in terms of compliance with air quality standards, particularly when comparing national thresholds with those established by the World Health Organization (WHO). The proposed methodology not only improves the accuracy of estimates but also enhances the interpretability of the factors driving air pollution dynamics. In addition to its academic and technical contributions, this study aims to provide accessible scientific evidence for the residents of both cities, raising awareness of the health risks associated with chronic exposure to air pollutants and encouraging informed actions to protect public health.
