3.5 Summary

We introduce conjugate family models for both discrete and continuous data. These models form the foundation of the Bayesian framework due to their mathematical tractability, as they provide closed-form expressions for the posterior distributions, marginal likelihood, and predictive distribution. Additionally, we present the Bayesian linear regression frameworks for both univariate and multivariate cases under conjugate families. These frameworks are fundamental for performing regression analysis in the Bayesian setting.