Bayesian modeling is a statistical approach that uses Bayes' theorem to update the likelihood of a hypothesis based on prior knowledge and new data. It is a powerful tool for analyzing complex systems and making predictions in a wide range of fields such as machine learning, artificial intelligence, psychology, economics, and biology. In Bayesian modeling, uncertainties in the data and assumptions are quantitatively accounted for, allowing for a more nuanced and flexible understanding of the underlying processes. This approach is particularly useful when dealing with small or incomplete datasets, as it provides a framework for incorporating prior knowledge and beliefs into the analysis.