Chapter 3 Cornerstone models: Conjugate families

We will introduce conjugate families, which are distributions for which the posterior distribution belongs to the same family as the prior distribution, given the likelihood. We provide some examples and solve them both analytically and computationally. We begin with simple examples of discrete and continuous distributions and then study the linear model in detail, both univariate and multivariate, deriving the posterior distributions, the marginal likelihood, and the predictive distribution analytically. Additionally, we will include mathematical and computational exercises in R.