Chapter 1 Basic formal concepts

We introduce formal concepts in Bayesian inference, beginning with Bayes’ rule and its components, along with their formal definitions and basic examples. In addition, we present key features of Bayesian inference, such as Bayesian updating and asymptotic sampling properties. We also cover the basics of Bayesian inference from a decision-theoretic perspective under uncertainty, introducing important concepts like loss functions, risk functions, and optimal decision rules.