In this paper, we present an alternative method to model the exceedances of the Colombian and global environmental standards for three pollutants, PM2.5, PM10 y O3, for the cities Colombia of Bogota´ and Medell´ın during the period of 2018-2020. The aforementioned is done using a stochastic model denominated the Non-Homogeneous Poisson Process with estimation employing Bayesian com putational methods. Through the usage of this methodology, it is intended to fit models with a highly predictive component for the case of Colombia and to allow interpretability through the parameters. Said methodology will allow for decisions to be made in terms of public policies. The best found models will, in the end, be all those that take into consideration the presence of two change-points or instants of variation. The change-points are given by the behavior of the country’s climate, public policies to mitigate pollution, the mandatory quarantine because of COVID-19 and infrastructure projects.