Bayesian inference is a statistical method for updating the probability of a hypothesis as more evidence or information becomes available. It provides a formal framework for probabilistic reasoning by utilizing Bayes' theorem to combine prior beliefs about parameters or hypotheses with the likelihood of observed data, yielding updated posterior probabilities that reflect the influence of the new evidence. This approach is significant for its principled method of incorporating prior knowledge and quantifying uncertainty, making it widely applicable across diverse research fields for parameter estimation, model comparison, and prediction.