Bayesian modeling is a statistical approach that uses Bayes' theorem to update the probability of a hypothesis as more evidence or information becomes available. It combines prior knowledge, represented as a prior probability, with new data to produce a posterior probability, which reflects the updated belief about the hypothesis. This method is particularly useful in situations where data is limited or uncertain. By incorporating prior beliefs and continuously updating them with new evidence, Bayesian modeling allows for more flexible and adaptive analysis in various fields, including machine learning, economics, and healthcare.