Posterior mean

This article explores the concept of the posterior mean in Bayesian statistics, illustrating how it serves as a weighted compromise between prior beliefs and observed data. It provides three concrete examples: the normal-normal model (using precision as weights), the beta-binomial model (using effective sample size), and the gamma-Poisson model (using time as weights). The content is technical, focusing on mathematical formulations and intuitive interpretations of Bayesian updating. It is relevant to IT/TECHNOLOGY as it covers statistical modeling and data science concepts used in machine learning, data analysis, and probabilistic programming.