posterior distribution

In Bayesian analysis, a posterior probability distribution is derived by combining prior information about a parameter with new evidence from a sample. This process uses Bayes's theorem to update the initial probability distribution, resulting in a revised distribution that reflects both the prior knowledge and the observed data. This posterior distribution then serves as the basis for statistical inferences about the parameter. The Bayesian approach allows for subjective or objective prior probabilities, making the subjectivity explicit, which is a point of contrast with classical statistics.123