a posteriori distribution

The a posteriori distribution is a concept within Bayesian analysis, a method of statistical inference. It represents a revised probability distribution for a parameter of interest after new evidence or sample information has been obtained and combined with a prior probability distribution using Bayes's theorem.12

In essence, it's a way to update beliefs based on new data. For example, if you have an initial idea about the likelihood of something (the prior distribution), and then you gather evidence, the a posteriori distribution shows your updated understanding of that likelihood. This process allows for statistical inferences to be made about the parameter, providing a basis for decision-making when faced with uncertainty.312