## 1.4 Summary: Chapter 1

In this chapter we introduce the Bayes’ rule to update probabilistic statements using funny examples. Then, we study the three probabilistic objects of main relevance in Bayesian inference: the posterior distribution, the marginal likelihood and the predictive density. The first allows performing inference regarding parameters, the second is required to perform hypothesis test for model selection using the Bayes factor, and the third to perform probabilistic predictions. We also review some sampling properties of Bayesian estimators, and Bayes update. All those concepts were developed using a simple example in R software. Finally, we introduce some concepts of decision theory that can be used to report summary statistics minimizing posterior expected losses.