## 1 Introduction  
Increasing urbanization and industrialization worldwide have heightened concerns about air quality due to rising emissions of atmospheric pollutants. With technological advancements and the expansion of industrial activities, the release of substances such as hydrogen sulfide or hydrogen sulfide gas (H\({}_{2}\)S), nitric oxide (NO), nitrogen dioxide (NO\({}_{2}\)), carbon dioxide (CO\({}_{2}\)), and sulfur dioxide (SO\({}_{2}\)) has become more frequent. These pollutants are known for their adverse impact on both the environment and human health [1]. Hydrogen sulfide is released primarily during industrial processes such as petroleum refineries and water and sewage treatment plants, and it occurs naturally in biological processes such as organic matter decomposition in waste deposits and wetlands. Furthermore, it is a substance known for its toxicity and can pose significant risks to human health when present in high concentrations [2]. On the other hand, carbon dioxide (CO\({}_{2}\)), a colorless, odorless, and non-flammable gas, is produced on a large scale by the industry, mainly as a byproduct in the production of ammonia and hydrogen, as well as in the burning of fossil fuels and petroleum refining. Although it can be used in some chemical reactions, CO\({}_{2}\) is known as the primary greenhouse gas, contributing significantly to climate change and global warming, becoming a globally recognized environmental concern [3; 4; 5]. In this context, gas adsorption has therefore become an area of great interest due to the need to develop more effective air purification systems. This process involves the adherence of atoms, molecules, or ions of substances (adsorbates) to a solid surface (adsorbent), resulting in the formation of a molecular or atomic layer on this surface. Adsorption has various applications, including water purification, separation of chemical compounds, and especially the capture of polluting gasses [6; 7; 8; 9]. The use of fixed-bed columns for adsorption is preferred in the industry due to their ability to treat large quantities of pollutants in a continuous flow system, enabling their implementation on a large scale. These columns provide breakthrough curves that describe the variation in pollutant concentration over time. Therefore, mathematical modeling of this system is important for understanding, analyzing, and optimizing separation and purification processes [10; 11; 12]. However, there are challenges in modeling continuous adsorption systems due to their non-linearity. Parameter estimation of the models often relies on linear regression techniques, including the method of least squares; however, such methods can distort parameter interpretation and compromise model assumptions [13]. Bayesian inference emerges as a promising alternative to least squares fitting, surpassing its limitations. This technique provides a method to combine available experimental data with mathematical modeling and the prior probability distribution of parameters. In general, it involves a statistical analysis of the posterior probability density, which represents the conditional probability of the parameters based on observations. The posterior probability density integrates the prior density of parameters--the information available before measurements--with the likelihood function, which expresses the probability of observations given the parameters in question [14; 15]. The posterior probability can be approximated through the Markov Chain Monte Carlo (MCMC) method, a computational tool for approximating integrals and generating samples from a posterior probability. The Metropolis-Hastings algorithm, widely used in MCMC, is based on the acceptance-rejection method and is effective in handling complex probability distributions, enabling random sampling from any probability distribution [16; 17].